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Abstract and Figures

Clustering structures appearing from small to large scales are ubiquitous in the physical world. Interestingly, clustering structures are omnipresent in human history too, ranging from the mere organization of life in societies (e.g., urbanization) to the development of large-scale infrastructure and policies for meeting organizational needs. Indeed, in its struggle for survival and progress, mankind has perpetually sought the benefits of unions. At the same time, it is acknowledged that as the scale of the projects grows, the cost of the delivered products is reduced while their quantities are maximized. Thus, large-scale infrastructures and policies are considered advantageous and are constantly being pursued at even great scales. This work develops a general method to quantify the temporal evolution of clustering, using a stochastic computational tool called 2D-C, which is applicable for the study of both natural and human social spatial structures. As case studies, the evolution of the structure of the universe, of ecosystems and of human clustering structures such as urbanization, are investigated using novel sources of spatial information. Results suggest the clear existence both of periods of clustering and declustering in the natural world and in the human social structures; yet clustering is the general trend. In view of the ongoing COVID-19 pandemic, societal challenges arising from large-scale clustering structures are discussed.
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sustainability
Article
Evolution of Clustering Quantified by a Stochastic
Method—Case Studies on Natural and Human
Social Structures
G.-Fivos Sargentis * , Theano Iliopoulou , Stavroula Sigourou, Panayiotis Dimitriadis and
Demetris Koutsoyiannis
Laboratory of Hydrology and Water Resources Development, School of Civil Engineering, National Technical
University of Athens, 157 80 Zographou, Greece; tiliopoulou@hydro.ntua.gr (T.I.); s.sigourou@gmail.com (S.S.);
pandim@itia.ntua.gr (P.D.); dk@itia.ntua.gr (D.K.)
*Correspondence: fivos@itia.ntua.gr
Received: 5 August 2020; Accepted: 14 September 2020; Published: 25 September 2020


Abstract:
Clustering structures appearing from small to large scales are ubiquitous in the physical
world. Interestingly, clustering structures are omnipresent in human history too, ranging from
the mere organization of life in societies (e.g., urbanization) to the development of large-scale
infrastructure and policies for meeting organizational needs. Indeed, in its struggle for survival and
progress, mankind has perpetually sought the benefits of unions. At the same time, it is acknowledged
that as the scale of the projects grows, the cost of the delivered products is reduced while their
quantities are maximized. Thus, large-scale infrastructures and policies are considered advantageous
and are constantly being pursued at even great scales. This work develops a general method to
quantify the temporal evolution of clustering, using a stochastic computational tool called 2D-C,
which is applicable for the study of both natural and human social spatial structures. As case studies,
the evolution of the structure of the universe, of ecosystems and of human clustering structures such
as urbanization, are investigated using novel sources of spatial information. Results suggest the clear
existence both of periods of clustering and declustering in the natural world and in the human social
structures; yet clustering is the general trend. In view of the ongoing COVID-19 pandemic, societal
challenges arising from large-scale clustering structures are discussed.
Keywords:
clustering evolution; natural clustering; social clustering; spatiotemporal clustering; scale
development; stochastic analysis
1. Introduction
«α
ετ
νµοῖονγει θε
ςςτ
νµοῖν» (Οδύσσεια,%218) [1]
“All ever, the god is bringing like and like together.” (Homer-Odyssey)
Seen from a stochastic viewpoint, both the evolution of the natural and the anthropogenic world
are marked by the emergence of various types of clustering in space, increasing and decreasing in
time. The existence of clustering can be claimed to be ubiquitous in the physical world, as it is found
in galaxies, in ecosystems, in the societies of humans and animals and even in the mere biological
organization of life. Indeed, we can see living creatures as the evolution of cells’ clustering: from the
appearance of bacteria (~3.6 billion years ago), protozoa (~1.7 billion years ago), fish (~0.45 billion
years ago), to dinosaurs (~0.25 billion years ago) to todays mammals (~0.22 billion years ago). [
2
5
].
Observing the omnipresent character of clustering structures, a first natural question that arises is: Is
clustering useful in life? complemented by the more central one: If yes, does it have a limit?
The first question has a seemingly straightforward answer. The plots in Figure 1give a first positive
reply to it. The average elephant, the biggest currently living animal on land, requires remarkably
Sustainability 2020,12, 7972; doi:10.3390/su12197972 www.mdpi.com/journal/sustainability
Sustainability 2020,12, 7972 2 of 22
less energy per mass than a mouse in order to survive (Figure 1a) as the bigger the animal, the more
eciently it uses energy [
6
,
7
]. Larger scales also seem to increase eciency for mammals in terms of
water consumption for survival (Figure 1b). Clustering is also useful in human societies, as clustering
of humans created what we now know as civilization. The clustering of human social processes along
with their increase in spatial scale, is a primary principle for the societal world. This is because human
clustering and interdependence structures enhance communication, promote science and exchange of
ideas, boost trade and reduce the cost of basic social goods (such as access to water and energy), thereby
improving the overall quality of human life [
8
10
]. In financial terms, the advantageous features of
increased clustering are expressed through the classic concept of “economies of scale” [11].
Sustainability 2020, 12, x FOR PEER REVIEW 2 of 22
the more efficiently it uses energy [6,7]. Larger scales also seem to increase efficiency for mammals in
terms of water consumption for survival (Figure 1b). Clustering is also useful in human societies, as
clustering of humans created what we now know as civilization. The clustering of human social
processes along with their increase in spatial scale, is a primary principle for the societal world. This
is because human clustering and interdependence structures enhance communication, promote
science and exchange of ideas, boost trade and reduce the cost of basic social goods (such as access to
water and energy), thereby improving the overall quality of human life [8,9,12]. In financial terms,
the advantageous features of increased clustering are expressed through the classic concept of
“economies of scale”[10].
(a) (b)
Figure 1. Daily energy consumption of mammals (a), Daily water consumption of mammals (b) data
from [11–15].
A more holistic inspection of natural evolution however reveals hidden elements of clustering,
which suggest that the second question also has a positive answer. Dinosaurs were the biggest living
creatures on earth but about 66 million years ago they disappeared. Smaller animals such as
mammals survived because of “Being small. If you're small you probably have a large population
and thus a wider genetic diversity.” [15]. Similar considerations might be drawn for human societies
regarding the rise and fall of civilizations, the population and depopulation of large cities, followed
by analogous trends in economic and agricultural activities over various spatial scales. The reasons
behind the reverse trend in the clustering tendency might be less discernible for the anthropogenic
world, however it becomes clear in this case as well that there is no single direction in terms of
clustering but rather there is a certain stochastic element dominating its evolution.
With the stochastic tool 2D-Climacogram (2D-C), clustering is quantified from each image
through cumulative variability over various scales, and a methodology is developed to allow the
characterization of its temporal evolution. In the literature, there are many approaches to quantify
clustering, calibrated for application in different fields as biology and ecosystems [16,17], life sciences
[18-21], neural networks [22], physics and physical phenomena [23,24], maps [25,26] and more [27],
yet there is no approach proposing a unifying stochastic view of 2D clustering in terms of variability
vs. scale. Moreover, while the presence of 2D clustering is studied as a behavior, its temporal
evolution is less explored as until recently, there was a scarcity of spatial information in time. Using
various sources of spatial information, such as animated maps [28,29] and satellite images, an effort
is made to characterize and interpret certain spatial aspects of the evolution of the natural and human
world that provide quantitative insights for understanding the past. This understanding might serve
as a basis for large-scale decision making for the future. This paper presents a stochastic methodology
that quantifies clustering in 2D space and its temporal evolution by analyzing image sequences of the
spatial structures over time.
We show the applicability of our tool in different fields by providing case studies from the
analysis of clustering in ecosystems i.e., the evolution of forests and water bodies, of human
structures, i.e., in terms of urbanization and urban expansion as well as in terms of cosmological
Figure 1.
Daily energy consumption of mammals (
a
), Daily water consumption of mammals (
b
) data
from [1215].
A more holistic inspection of natural evolution however reveals hidden elements of clustering,
which suggest that the second question also has a positive answer. Dinosaurs were the biggest living
creatures on earth but about 66 million years ago they disappeared. Smaller animals such as mammals
survived because of “Being small. If you’re small you probably have a large population and thus a
wider genetic diversity.” [
15
]. Similar considerations might be drawn for human societies regarding
the rise and fall of civilizations, the population and depopulation of large cities, followed by analogous
trends in economic and agricultural activities over various spatial scales. The reasons behind the
reverse trend in the clustering tendency might be less discernible for the anthropogenic world, however
it becomes clear in this case as well that there is no single direction in terms of clustering but rather
there is a certain stochastic element dominating its evolution.
With the stochastic tool 2D-Climacogram (2D-C), clustering is quantified from each image through
cumulative variability over various scales, and a methodology is developed to allow the characterization
of its temporal evolution. In the literature, there are many approaches to quantify clustering, calibrated
for application in dierent fields as biology and ecosystems [
16
,
17
], life sciences [
18
21
], neural
networks [
22
], physics and physical phenomena [
23
,
24
], maps [
25
,
26
] and more [
27
], yet there is
no approach proposing a unifying stochastic view of 2D clustering in terms of variability vs. scale.
Moreover, while the presence of 2D clustering is studied as a behavior, its temporal evolution is
less explored as until recently, there was a scarcity of spatial information in time. Using various
sources of spatial information, such as animated maps [
28
,
29
] and satellite images, an eort is made
to characterize and interpret certain spatial aspects of the evolution of the natural and human world
that provide quantitative insights for understanding the past. This understanding might serve as a
basis for large-scale decision making for the future. This paper presents a stochastic methodology
that quantifies clustering in 2D space and its temporal evolution by analyzing image sequences of the
spatial structures over time.
Sustainability 2020,12, 7972 3 of 22
We show the applicability of our tool in dierent fields by providing case studies from the analysis
of clustering in ecosystems i.e., the evolution of forests and water bodies, of human structures, i.e., in
terms of urbanization and urban expansion as well as in terms of cosmological simulations. The latter
provide a very relevant quantification of clustering as the evolution of clustering in universe is widely
studied [3034] and it can be viewed as a macroscopic picture of clustering in nature.
We conclude our work with a theoretical discussion on the role of clustering in the human social
structure. In view of the COVID-19 pandemic, we discuss the risk dynamics stemming from large-scale
human clustering. Furthermore, by considering the way the latter was mitigated, i.e., through the
destruction of large-scale social clustering structures, we draw wider considerations on the existence
of an “optimal” scale and spatial distribution for human organization and society development.
2. Methodology
2.1. Stochastic Analysis of Clustering in 2D Space: The 2D-C Tool
The mathematical field of Stochastics has been introduced on the opposite side of deterministic
approaches, as a way to model the so-called random, i.e., complex, unexplained or unpredictable,
fluctuations observed in non-linear geophysical processes [
35
,
36
]. Stochastics helps to develop a
unified perception of natural phenomena and expel dichotomies like random vs. deterministic. From
the viewpoint of stochastics, there is no such thing as a “virus of randomness” that infects some
phenomena to make them random, leaving other phenomena uninfected. Instead, both randomness
and predictability coexist and are intrinsic to natural systems which can be deterministic and random
at the same time, depending on the prediction horizon and the time scale [
37
]. This research aims to
develop a stochastic analysis method to quantify both the spatial structures in terms of clustering and
the temporal evolution thereof.
A stochastic computational tool called 2D-Climacogram, abbreviated as 2D-C [
38
,
39
], is used to
study the clustering in 2D space, using images from various sources. 2D-C measures the degree of
variability (change in variability vs. scale) in images using stochastic analysis. Here, we refer to spatial
scale, defined as the ratio of the area of k
×
kadjacent cells (i.e., scale k) that are averaged to form the
(scaled) spatial field, over the spatial resolution of the original field (i.e., at scale 1).
Image processing typically begins with filtering or enhancing an image using techniques to extract
more information from the images [
40
] and image segmentation is one of the basic problems in image
analysis. The importance and utility of image segmentation has resulted in extensive research and
numerous proposed approaches based on intensity, color, texture etc. that are both automatic and
interactive [41].
This analysis for image processing is based on a stochastic tool called climacogram. The term
climacogram [
42
,
43
] comes from the Greek word climax (meaning scale). It is defined as the (plot of)
variance of the averaged process (assuming stationary) versus the averaging scale kand is denoted
as
γ
(k). The climacogram is useful for detecting both the short- and the long-term change (or else
dependence, persistence and clustering) of a process, with the latter emerging particularly in complex
systems as opposed to white-noise (absence of dependence) or Markov (i.e., short-range dependence)
behavior [44].
In order to quantify the image variability, each image was first digitized in two dimensions (2D)
based on the grayscale color intensity (thus, studying the brightness of an image), and the climacogram
was calculated based on the geometric scales of adjacent pixels. Assuming that our sample is an area
n
×
n
, where nis the number of intervals (e.g., pixels) along each spatial direction and
is the
discretization unit (determined by the image resolution, e.g., pixel length), the empirical classical
estimator of the climacogram for a 2D process can be expressed in equation 1 as:
ˆ
γ(κ)=1
n2/κ21
n/κ
X
i=1
n/κ
X
j=1x(κ)
i,jx2
(1)
Sustainability 2020,12, 7972 4 of 22
where the ‘ˆ’ over
γ
denotes an estimate,
κ
is the dimensionless spatial scale,
x(κ)
i,j=
1
κ2Pκj
ψ=κ(j1)+1Pκi
ξ=κ(i1)+1xξ,ψ
represents a local average of the space-averaged process at scale
κ
, and at grid cell (i,j),
xx(n)
1,1
is the global average and the underlined variables represent random
variables as opposed to regular ones. Note that the maximum available scale for this estimator is n/2.
The dierence between the value in each element and the field mean is raised to the power of 2, since
we are mostly interested in the magnitude of the dierence rather than its sign, and in particular, in
the variance estimation. Therefore, the 2D-C expressed the diversity in the color intensity among the
dierent elements at each scale by quantifying the variability of their brightness intensities.
An important property of stochastic processes which characterizes the variability over scales is the
Hurst–Kolmogorov (HK) behavior (persistence), which can be represented by the Hurst parameter [
45
].
This parameter can be estimated by minimizing the fitting error between the empirical (observed) and
the modeled (Equation (2)) climacogram, both of which are derived from the large-scale values, i.e.,
the last 50 scales are used in the presented applications. The isotropic HK process with an arbitrary
marginal distribution, i.e., the power-law decay of variance as a function of scale, can be defined for a
1D or 2D process as:
γ(k)=λ
(k/)2d(1H)(2)
where
λ
is the variance at scale k=
,
is the time or space unit, dis the dimensionality of the
process/field (i.e., for a 1D process d=1, for a 2D field d=2, etc.) and His the Hurst parameter
(0 <H<1)
. For 0 <H<0.5 the HK process exhibits an anti-persistent behavior, H=0.5 corresponds to
the white noise process and for 0.5 <H<1 the process exhibits persistence (i.e., clustering). In the
case of clustering behavior due to heterogeneity of the brightness of the image, the high variability in
brightness persists even in large scales. This clustering eect may substantially increase the diversity
between the brightness in each pixel of the image, a phenomenon also observed in hydrometeorological
processes (such as temperature, precipitation, wind etc. [36]), natural landscapes and music [46].
The algorithm that generates the climacogram in 2D was developed in MATLAB for rectangular
images [
47
]. In particular, for the current analysis, the images are cropped to 400
×
400 pixels, 14.11 cm
×14.11 cm, in 72 dpi (dots per inch).
2.2. Temporal Evolution of 2D Clustering
The pixels analyzed are represented by numbers denoting their color intensity in grayscale (white
=1, black =0). Figure 2presents images from three timeframes of the evolution of the universe as
generated by a cosmological model of evolution [
48
]: (a) 500 million years after Big Bang, an image
with faint clustering; (b) 1000 million years after the Big Bang, an image with clustering and (c) 10,000
million years after the Big Bang, an image with intense clustering. Figure 3presents the steps of
analysis and shows grouped pixels at scales k=2, 4, 8, 16, 20, 25, 40, 50, 80, 100 and 200 that were used
to calculate the climacogram.
The presence of clustering is reflected in the climacogram, which shows a marked dierence as
clustering increases (Figure 4a,b). Specifically, the variance of the images is notably higher at all scales
when clustering increases, indicating a greater degree of variability of the process.
For the integration of all information contained in the 2D climacogram of each timeframe, we
evaluated the cumulative areas underneath each one for all scales (Figure 5a), i.e., the climacogram
integral
Rk
γ(x)/xdx
, where
and kare the minimum and maximum scale and we have divided by x
in order for the integral to converge for an arbitrarily high k(
k→ ∞
). In the discrete case, this can be
approximated as in Equation (3):
CI(k)=
n(k)1
X
i=1
2γ(xi)xi+1xi
xi+1+xi
(3)
Sustainability 2020,12, 7972 5 of 22
where
n(k)
is the number of integration intervals up to scale k. We evaluated
CI(k)
at the maximum
available spatial scale, in order for it to be the best approximation of the limit CI().
Sustainability 2020, 12, x FOR PEER REVIEW 5 of 22
(a) (b) (c)
Figure 2. Benchmark of image analysis, evolution of the universe [48]: (a) an image of 500 million
years after the Big Bang with faint clustering and an average brightness of 0.45; (b) an image of 1000
million years after the Big Bang with clustering and an average brightness of 0.44; (c) an image of
10,000 million years after the Big Bang image with intense clustering and an average brightness of
0.33 (snapshots from videos of cosmological simulations, [48,49]).
Figure 3. Example of stochastic analysis of a 2D picture, in escalating spatial scales, as shown on the
left in red. Grouped pixels at different scales are used to calculate the climacogram: (a) images (a), (b)
and (c) correspond to times as given in Figure 1.
Figure 2.
Benchmark of image analysis, evolution of the universe [
48
]: (
a
) an image of 500 million years
after the Big Bang with faint clustering and an average brightness of 0.45; (
b
) an image of 1000 million
years after the Big Bang with clustering and an average brightness of 0.44; (
c
) an image of 10,000 million
years after the Big Bang image with intense clustering and an average brightness of 0.33 (snapshots
from videos of cosmological simulations, [48,49]).
Figure 3.
Example of stochastic analysis of a 2D picture, in escalating spatial scales, as shown on the
left in red. Grouped pixels at dierent scales are used to calculate the climacogram: images (
a
), (
b
) and
(c) correspond to times as given in Figure 2.
Sustainability 2020,12, 7972 6 of 22
Sustainability 2020, 12, x FOR PEER REVIEW 6 of 22
(a) (b)
Figure 4. (a) Climacograms of the benchmark images; (b) standardized climacograms of the
benchmark images. A standardized climacogram is not helpful for evaluating the range of the
evolution of clustering but is helpful to estimate curves’ slopes for further stochastic analysis.
(a) (b)
Figure 5. (a) Cumulative areas underneath each climacogram for each scale; (b) Rate of alteration of
clustering through time.
In Figure 5b, each climacogram is represented by the respective integral, thus we can evaluate
the rate of alteration of clustering through time.
3. Case Studies
In order to present the applicability of our tool in different fields, we studied several examples
as case studies illustrating clustering in nature from cosmological simulations as well as in
ecosystems and human social structures such as the evolution of urbanization and urban expansion.
0.000001
0.00001
0.0001
0.001
0.01
0.1
110100
γ(k)
k
(c)
(b)
(a)
0.01
0.1
1
110100
γ(k)
k
White noise
(c)
(b)
(a)
(a) (b)
(
c
)
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
0.045
0.05
500
Climacogram integral
Million years since Big Bang
10000
Figure 4.
(
a
) Climacograms of the benchmark images; (
b
) standardized climacograms of the benchmark
images. A standardized climacogram is not helpful for evaluating the range of the evolution of
clustering but is helpful to estimate curves’ slopes for further stochastic analysis.
Sustainability 2020, 12, x FOR PEER REVIEW 6 of 22
(a) (b)
Figure 4. (a) Climacograms of the benchmark images; (b) standardized climacograms of the
benchmark images. A standardized climacogram is not helpful for evaluating the range of the
evolution of clustering but is helpful to estimate curves’ slopes for further stochastic analysis.
(a) (b)
Figure 5. (a) Cumulative areas underneath each climacogram for each scale; (b) Rate of alteration of
clustering through time.
In Figure 5b, each climacogram is represented by the respective integral, thus we can evaluate
the rate of alteration of clustering through time.
3. Case Studies
In order to present the applicability of our tool in different fields, we studied several examples
as case studies illustrating clustering in nature from cosmological simulations as well as in
ecosystems and human social structures such as the evolution of urbanization and urban expansion.
0.000001
0.00001
0.0001
0.001
0.01
0.1
110100
γ(k)
k
(c)
(b)
(a)
0.01
0.1
1
110100
γ(k)
k
White noise
(c)
(b)
(a)
(a) (b)
(
c
)
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
0.045
0.05
500
Climacogram integral
Million years since Big Bang
10000
Figure 5.
(
a
) Cumulative areas underneath each climacogram for each scale; (
b
) Rate of alteration of
clustering through time.
In Figure 5b, each climacogram is represented by the respective integral, thus we can evaluate the
rate of alteration of clustering through time.
3. Case Studies
In order to present the applicability of our tool in dierent fields, we studied several examples as
case studies illustrating clustering in nature from cosmological simulations as well as in ecosystems
and human social structures such as the evolution of urbanization and urban expansion.
Sustainability 2020,12, 7972 7 of 22
3.1. Evolution of Clustering in Nature
3.1.1. Cosmological Simulations
Some cosmological simulations of the growth of Black Holes and Galaxies [
48
] show that the
evolution of the universe is characterized by a tendency for clustering through time [
34
]. We analyzed
timeframes of a general view of one cosmological simulation model (Figure S1: General view of the
direct Cosmological Simulations of the Growth of Black Holes and Galaxies [
48
,
49
]) and a closer zoom
(Figure S3: Closer zoom in an area of the direct Cosmological Simulations of the Growth of Black Holes
and Galaxies) using 2D-C plots (Figure S2: Climacograms of the Direct Cosmological Simulations of
the Growth of Black Holes and Galaxies (Figure S1) and Figure S4: Climacograms of the closer zoom of
Direct Cosmological Simulations of the Growth of Black Holes and Galaxies (Figure S2)). We evaluated
the temporal evolution of clustering by following the methodology of Section 2, i.e., we found the
cumulative areas underneath each time-referenced climacogram and plotted the temporal evolution of
the integrals (Figure 6).
Sustainability 2020, 12, x FOR PEER REVIEW 7 of 22
3.1. Evolution of Clustering in Nature
3.1.1. Cosmological Simulations
Some cosmological simulations of the growth of Black Holes and Galaxies [49] show that the
evolution of the universe is characterized by a tendency for clustering through time [34]. We analyzed
timeframes of a general view of one cosmological simulation model (Figure S1) and a closer zoom
(Figure S3) using 2D-C plots (Figure S2 and S4). We evaluated the temporal evolution of clustering
by following the methodology of Section 2, i.e., we found the cumulative areas underneath each time-
referenced climacogram and plotted the temporal evolution of the integrals (Figure 6).
In addition, we evaluated the clustering behavior shown in the Millennium Simulation Project
[51] (Figure S5). Specifically, the Millennium simulation Project shows four timeframes of the
evolution of a projected density field, with three different views. To unify the study of the stochastic
behavior from the three distinct cosmological views of Millennium Simulation Project (772 Mpc/h,
193 Mpc/h, 48.25 Mpc/h) we employed the following procedure. For each scale, we formed the sample
of empirical climacogram values estimated from each of the three series. For the range of scales at
which the series overlap we matched the respective climacogram values with one another by
minimizing the sum of their sample standard deviations for the given scales. For the (unconstrained)
minimization we used the Generalized Reduced Gradient method [51,52] which is one of the most
robust and reliable approaches to nonlinear optimization [53] (Figure S6).
Figure 6. Rate of alteration of clustering through time of image series in figures S1, S3, S5.
3.1.2. Ecosystems
Ecosystems are characterized by dynamic transformations involving spatial clustering. In order to
show how the proposed stochastic tool could be applied in the study of ecosystems, we present the
quantification of the evolution of clustering for three case studies: (a) the deforestation of Borneo
(Figure 7, 9a S8, S9, S10), (b) the deforestation of the Amazon (Figure 8, 9b, S11, S12, S13) and (c) the
evolution of water bodies in Greece (Figure 10, 11, S14, S15, S16). In these examples, we can see the
demolition of the forests’ clustering in Borneo, and the evolution of clustering of dry lands and urban
areas in the Amazon forest. An interesting insight is provided, showing the evolution of water bodies
in Greece, as new artificial lakes are created, resulting in amplification of natural variability. Such an
argument in favor of the integration of dams in the landscape was recently proposed [54]. Note that
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0 5000 10000 15000
Climacogram integral
Million years since the Big Bang
Evolution of the universe, general view
Evolution of the universe, zoom view
Millennium Simulation Project 772 Mpc/h
Millennium Simulation Project 193 Mpc/h
Millennium Simulation Project 42.25 Mpc/h
Millennium Simulation Project, composed climacograms
Figure 6. Rate of alteration of clustering through time of image series in Figures S1, S3, S5.
In addition, we evaluated the clustering behavior shown in the Millennium Simulation Project [
50
]
(Figure S5: Evolution of the universe. Millennium Simulation Project [
50
]). Specifically, the Millennium
simulation Project shows four timeframes of the evolution of a projected density field, with three
dierent views. To unify the study of the stochastic behavior from the three distinct cosmological views
of Millennium Simulation Project (772 Mpc/h, 193 Mpc/h, 48.25 Mpc/h) we employed the following
procedure. For each scale, we formed the sample of empirical climacogram values estimated from
each of the three series. For the range of scales at which the series overlap we matched the respective
climacogram values with one another by minimizing the sum of their sample standard deviations for
the given scales. For the (unconstrained) minimization we used the Generalized Reduced Gradient
method [
51
,
52
] which is one of the most robust and reliable approaches to nonlinear optimization [
53
]
(Figure S6: Fitting curves of composed climacograms of Millennium Simulation Project [
50
] (a) image
series of 210 mil years after B.B.; (b) image series of 1000 mil years after B.B.; (c) image series of 4700 mil
years after B.B.; (d) image series of 13,600 mil years after B.B.).
Sustainability 2020,12, 7972 8 of 22
3.1.2. Ecosystems
Ecosystems are characterized by dynamic transformations involving spatial clustering. In order
to show how the proposed stochastic tool could be applied in the study of ecosystems, we present the
quantification of the evolution of clustering for three case studies:
the deforestation of Borneo, Figures 7, 9a, S8: Deforestation in Borneo 1950–2005 (a) 1950; (b)
1985; (c) 2000 (d) 2005 [
54
], Figure S9: Climacograms of the deforestation in Borneo, Figure
S10: Evaluation of climacograms and rhythm of clustering in demolition of fosters’ clustering
in Borneo,
the deforestation of the Amazon, Figures 8,9b, S11: Deforestation of Amazon, creation of clustering
of dry land and urban areas inside forest [
55
], Figure S12: Climacograms of the deforestation in
Amazon, Figure S13: Evaluation of climacograms and rhythm of clustering evolution of dry-lands’
clustering in Amazon
the evolution of water bodies in Greece, Figures 10,11, S14: Greece, natural and artificial lakes (a)
overview map of the area with natural and artificial lakes in 2020; (b) layer of the map; natural and
artificial lakes 2020; (c) layer of the map; lakes 2020, Figure S15: Evolution of water bodies in Greece
as new big dams are constructed and new artificial lakes are created, Figure S16: Climacograms of
the evolution of water bodies in Greece.
In these examples, we can see the demolition of the forests’ clustering in Borneo, and the evolution
of clustering of dry lands and urban areas in the Amazon forest. An interesting insight is provided,
showing the evolution of water bodies in Greece, as new artificial lakes are created, resulting in
amplification of natural variability. Such an argument in favor of the integration of dams in the
landscape was recently proposed [
56
]. Note that increasing clustering of water bodies is associated
with the construction of large-scale dams and it is related to the economic growth; increasing clustering
appears in periods of increasing Gross Domestic Product (GDP) (Figure 11).
Sustainability 2020, 12, x FOR PEER REVIEW 8 of 22
is related to the economic growth; increasing clustering appears in periods of increasing Gross
Domestic Product (GDP) (Figure 11).
(a) (b) (c) (d)
Figure 7. Deforestation in Borneo, declustering of forests 1950-2005 (a) 1950; (b) 1985; (c) 2000 (d) 2005
[53].
(a) (b) (c) (d) (e)
Figure 8. Deforestation of the Amazon, creation of clustering of dry land and urban areas inside a
forest (a) 1984; (b) 1992; (c) 2000; (d) 2008; (e) 2016 [56].
(a) (b)
Figure 9. Rate of alteration of clustering through time of (a) demolition of fosters’ clustering in Borneo;
data from Figure S8 (b) evolution of dry-lands’ clustering in the Amazon; data from Figure S11.
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
1950 1980 2010
Climacogram integral
0
0.01
0.02
0.03
0.04
0.05
0.06
1984 1994 2004 2014
Climacogram integral
Figure 7.
Deforestation in Borneo, declustering of forests 1950–2005 (
a
) 1950; (
b
) 1985; (
c
) 2000 (
d
)
2005 [54].
Sustainability 2020, 12, x FOR PEER REVIEW 8 of 22
is related to the economic growth; increasing clustering appears in periods of increasing Gross
Domestic Product (GDP) (Figure 11).
(a) (b) (c) (d)
Figure 7. Deforestation in Borneo, declustering of forests 1950-2005 (a) 1950; (b) 1985; (c) 2000 (d) 2005
[53].
(a) (b) (c) (d) (e)
Figure 8. Deforestation of the Amazon, creation of clustering of dry land and urban areas inside a
forest (a) 1984; (b) 1992; (c) 2000; (d) 2008; (e) 2016 [56].
(a) (b)
Figure 9. Rate of alteration of clustering through time of (a) demolition of fosters’ clustering in Borneo;
data from Figure S8 (b) evolution of dry-lands’ clustering in the Amazon; data from Figure S11.
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
1950 1980 2010
Climacogram integral
0
0.01
0.02
0.03
0.04
0.05
0.06
1984 1994 2004 2014
Climacogram integral
Figure 8.
Deforestation of the Amazon, creation of clustering of dry land and urban areas inside a
forest (a) 1984; (b) 1992; (c) 2000; (d) 2008; (e) 2016 [55].
Sustainability 2020,12, 7972 9 of 22
Sustainability 2020, 12, x FOR PEER REVIEW 8 of 22
is related to the economic growth; increasing clustering appears in periods of increasing Gross
Domestic Product (GDP) (Figure 11).
(a) (b) (c) (d)
Figure 7. Deforestation in Borneo, declustering of forests 1950-2005 (a) 1950; (b) 1985; (c) 2000 (d) 2005
[53].
(a) (b) (c) (d) (e)
Figure 8. Deforestation of the Amazon, creation of clustering of dry land and urban areas inside a
forest (a) 1984; (b) 1992; (c) 2000; (d) 2008; (e) 2016 [56].
(a) (b)
Figure 9. Rate of alteration of clustering through time of (a) demolition of fosters’ clustering in Borneo;
data from Figure S8 (b) evolution of dry-lands’ clustering in the Amazon; data from Figure S11.
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
1950 1980 2010
Climacogram integral
0
0.01
0.02
0.03
0.04
0.05
0.06
1984 1994 2004 2014
Climacogram integral
Figure 9.
Rate of alteration of clustering through time of (
a
) demolition of fosters’ clustering in Borneo;
data from Figure S8 (b) evolution of dry-lands’ clustering in the Amazon; data from Figure S11.
Sustainability 2020, 12, x FOR PEER REVIEW 9 of 22
(a) (b) (c)
Figure 10. Evolution of water bodies in Greece as new artificial lakes are created (a) overview map of
the area with natural and artificial lakes in 2020; (b) layer of the map: lakes in 1960; (c) layer of the
map: lakes in 2020.
Figure 11. Rate of alteration of clustering through time of water bodies in Greece through the
construction of large dams; related to the GDP of Greece; data from Figure S14.
3.2. Evolution of Human Social Clustering
Large-scale infrastructure projects are necessary when the human population is clustered and
organized in large units. In order to understand and describe the changing scale of infrastructures, it
is necessary to first assess the evolution of human social clustering. This is facilitated through the
investigation of spatial databases. To this aim, we employed our stochastic methodology to
characterize the temporal evolution of spatial information regarding human social clustering.
The beginning of human civilization is signaled by the organization of systematic agriculture
through the clustering of cropland areas (Figures 12, S18) and the formation of human clustering
structures, i.e., societies that stabilized in space forming cities and transforming their environment
(Figure 13, S20). We evaluated related historical data to quantify the evolution of clustering at the
global (Figure 14a, S19 S22a) and local scale (Figure 14b, S21, S22b). Figure 14a shows the evolution
of cropland areas from 1000 BC to 2000 AD worldwide, derived from [57], whereas Figure 14b shows
the evolution of settlements in London from 1 AD to 1900 AD, derived from [58]. It is interesting to
note the radical increase in the rate of clustering occurring in both cases after 1700 AD (Figure 14),
i.e., in the period after the industrial revolution.
0
50
100
150
200
250
300
350
0.002
0.002
0.002
0.002
0.002
0.003
0.003
0.003
0.003
0.003
0.003
1930 1950 1970 1990 2010
GDP of Greece (Billion $)
Climacogram integral
Climacogram integral GDP of Greece (Billion $)
Figure 10. Evolution of water bodies in Greece as new artificial lakes are created (a) overview map of
the area with natural and artificial lakes in 2020; (
b
) layer of the map: lakes in 1960; (
c
) layer of the map:
lakes in 2020.
Sustainability 2020, 12, x FOR PEER REVIEW 9 of 22
(a) (b) (c)
Figure 10. Evolution of water bodies in Greece as new artificial lakes are created (a) overview map of
the area with natural and artificial lakes in 2020; (b) layer of the map: lakes in 1960; (c) layer of the
map: lakes in 2020.
Figure 11. Rate of alteration of clustering through time of water bodies in Greece through the
construction of large dams; related to the GDP of Greece; data from Figure S14.
3.2. Evolution of Human Social Clustering
Large-scale infrastructure projects are necessary when the human population is clustered and
organized in large units. In order to understand and describe the changing scale of infrastructures, it
is necessary to first assess the evolution of human social clustering. This is facilitated through the
investigation of spatial databases. To this aim, we employed our stochastic methodology to
characterize the temporal evolution of spatial information regarding human social clustering.
The beginning of human civilization is signaled by the organization of systematic agriculture
through the clustering of cropland areas (Figures 12, S18) and the formation of human clustering
structures, i.e., societies that stabilized in space forming cities and transforming their environment
(Figure 13, S20). We evaluated related historical data to quantify the evolution of clustering at the
global (Figure 14a, S19 S22a) and local scale (Figure 14b, S21, S22b). Figure 14a shows the evolution
of cropland areas from 1000 BC to 2000 AD worldwide, derived from [57], whereas Figure 14b shows
the evolution of settlements in London from 1 AD to 1900 AD, derived from [58]. It is interesting to
note the radical increase in the rate of clustering occurring in both cases after 1700 AD (Figure 14),
i.e., in the period after the industrial revolution.
0
50
100
150
200
250
300
350
0.002
0.002
0.002
0.002
0.002
0.003
0.003
0.003
0.003
0.003
0.003
1930 1950 1970 1990 2010
GDP of Greece (Billion $)
Climacogram integral
Climacogram integral GDP of Greece (Billion $)
Figure 11.
Rate of alteration of clustering through time of water bodies in Greece through the
construction of large dams; related to the GDP of Greece; data from Figure S14.
Sustainability 2020,12, 7972 10 of 22
3.2. Evolution of Human Social Clustering
Large-scale infrastructure projects are necessary when the human population is clustered and
organized in large units. In order to understand and describe the changing scale of infrastructures,
it is necessary to first assess the evolution of human social clustering. This is facilitated through the
investigation of spatial databases. To this aim, we employed our stochastic methodology to characterize
the temporal evolution of spatial information regarding human social clustering.
The beginning of human civilization is signaled by the organization of systematic agriculture
through the clustering of cropland areas (Figures 12, S18: Evolution of cropland area; historical data
from 3000 BC to AD 2000. [
57
]) and the formation of human clustering structures, i.e., societies that
stabilized in space forming cities and transforming their environment (Figures 13, S20: Evolution of
London; historical data from 1 AD to 1950 AD. [58]). We evaluated related historical data to quantify
the evolution of clustering at the global (Figures 14a, S19: Climacograms of cropland areas, Figure
S22a: Evaluation of climacograms and rhythm of clustering of cropland land historical data) and local
scale (Figures 14b, S21: Climacograms. Clustering of urbanization of London, Figure S22b: Evaluation
of climacograms and rhythm of clustering and evolution of urbanization in London area).
Figure 14a shows the evolution of cropland areas from 1000 BC to 2000 AD worldwide, derived
from [
57
], whereas Figure 14b shows the evolution of settlements in London from 1 AD to 1900 AD,
derived from [
58
]. It is interesting to note the radical increase in the rate of clustering occurring in both
cases after 1700 AD (Figure 14), i.e., in the period after the industrial revolution.
It should be noted however that threats such as natural disasters and war demolish clustering of
human social structures, as revealed by the inspection of satellite lights in Syria after the onset of the
civil war (Figures 15, S40: Satellite night lights of Syria taken from Reference [
59
]; (
a
) 2012; (b) 2014; (
c
)
Rate of alteration of clustering after the onset of the civil war).
Sustainability 2020, 12, x FOR PEER REVIEW 10 of 22
(a) (b) (c) (d)
Figure 12. Evolution of cropland area; historical data (a) 1000 BC; (b) 1000AD; (c) 1700AD (d) 2000
[57].
(a) (b) (c) (d) (e)
Figure 13. Evolution of London; historical data (a) 1AD; (b) 1500AD; (c) 1700AD; (d) 1850AD;
(e)1900AD [58].
(a) (b)
Figure 14. Rate of alteration of clustering through time of (a) cropland land historical data (b)
evolution of urbanization in the London area.
It should be noted however that threats such as natural disasters and war demolish clustering
of human social structures, as revealed by the inspection of satellite lights in Syria after the onset of
the civil war (Figure 15, S40).
(a) (b) (c)
Figure 15. Satellite night lights of Syria taken from Reference [59]; (a) 2012; (b) 2014; (c) Rate of
alteration of clustering after the onset of the civil war.
Figure 12.
Evolution of cropland area; historical data (
a
) 1000 BC; (
b
) 1000AD; (
c
) 1700AD (
d
) 2000 [
57
].
Sustainability 2020, 12, x FOR PEER REVIEW 10 of 22
(a) (b) (c) (d)
Figure 12. Evolution of cropland area; historical data (a) 1000 BC; (b) 1000AD; (c) 1700AD (d) 2000
[57].
(a) (b) (c) (d) (e)
Figure 13. Evolution of London; historical data (a) 1AD; (b) 1500AD; (c) 1700AD; (d) 1850AD;
(e)1900AD [58].
(a) (b)
Figure 14. Rate of alteration of clustering through time of (a) cropland land historical data (b)
evolution of urbanization in the London area.
It should be noted however that threats such as natural disasters and war demolish clustering
of human social structures, as revealed by the inspection of satellite lights in Syria after the onset of
the civil war (Figure 15, S40).
(a) (b) (c)
Figure 15. Satellite night lights of Syria taken from Reference [59]; (a) 2012; (b) 2014; (c) Rate of
alteration of clustering after the onset of the civil war.
Figure 13.
Evolution of London; historical data (
a
) 1AD; (
b
) 1500AD; (
c
) 1700AD; (
d
) 1850AD;
(e) 1900AD [58].
Sustainability 2020,12, 7972 11 of 22
Sustainability 2020, 12, x FOR PEER REVIEW 10 of 22
(a) (b) (c) (d)
Figure 12. Evolution of cropland area; historical data (a) 1000 BC; (b) 1000AD; (c) 1700AD (d) 2000
[57].
(a) (b) (c) (d) (e)
Figure 13. Evolution of London; historical data (a) 1AD; (b) 1500AD; (c) 1700AD; (d) 1850AD;
(e)1900AD [58].
(a) (b)
Figure 14. Rate of alteration of clustering through time of (a) cropland land historical data (b)
evolution of urbanization in the London area.
It should be noted however that threats such as natural disasters and war demolish clustering
of human social structures, as revealed by the inspection of satellite lights in Syria after the onset of
the civil war (Figure 15, S40).
(a) (b) (c)
Figure 15. Satellite night lights of Syria taken from Reference [59]; (a) 2012; (b) 2014; (c) Rate of
alteration of clustering after the onset of the civil war.
Figure 14.
Rate of alteration of clustering through time of (
a
) cropland land historical data (
b
) evolution
of urbanization in the London area.
Sustainability 2020, 12, x FOR PEER REVIEW 10 of 22
(a) (b) (c) (d)
Figure 12. Evolution of cropland area; historical data (a) 1000 BC; (b) 1000AD; (c) 1700AD (d) 2000
[57].
(a) (b) (c) (d) (e)
Figure 13. Evolution of London; historical data (a) 1AD; (b) 1500AD; (c) 1700AD; (d) 1850AD;
(e)1900AD [58].
(a) (b)
Figure 14. Rate of alteration of clustering through time of (a) cropland land historical data (b)
evolution of urbanization in the London area.
It should be noted however that threats such as natural disasters and war demolish clustering
of human social structures, as revealed by the inspection of satellite lights in Syria after the onset of
the civil war (Figure 15, S40).
(a) (b) (c)
Figure 15.
Satellite night lights of Syria taken from Reference [
59
]; (
a
) 2012; (
b
) 2014; (
c
) Rate of
alteration of clustering after the onset of the civil war.
Next, we explored spatial data pertaining to urbanization taking place in the past century. The first
information source examined was the spatial distribution of satellite night lights. The night lights have
been widely used as an index of the population and density of settlements [
60
], economic activity [
61
],
consumption and distribution of electricity [
62
], poverty and development status [
63
] and human
exposure to natural disasters such as floods [
64
]. An example showing satellite images from city lights
in Europe is shown in Figure 16, while their respective climacograms are shown in Figure 17.
Sustainability 2020, 12, x FOR PEER REVIEW 11 of 22
Next, we explored spatial data pertaining to urbanization taking place in the past century. The
first information source examined was the spatial distribution of satellite night lights. The night lights
have been widely used as an index of the population and density of settlements [60], economic
activity [61], consumption and distribution of electricity [62], poverty and development status [63]
and human exposure to natural disasters such as floods [64]. An example showing satellite images
from city lights in Europe is shown in Figure 16, while their respective climacograms are shown in
Figure 17.
(a) (b) (c) (d)
Figure 16. (a) Europe and its night lights in (b) 1992, (c) 2002, (d) 2012.
Figure 17. Climacograms of the images of night lights of Europe.
The second information source examined was the spatial dataset on land uses. Large-scale
geospatial data, including land-cover types, were obtained from the Historical Database of the Global
Environment, HYDE 3.1 [57], of the National Centers For Environmental Information at the National
Oceanic And Atmospheric Administration (NOAA). HYDE datasets are based on Food and
Agriculture Organization of the United Nations agricultural statistics and land use (FAOSTAT) over
the period 1960–2010 [65], a variety of other historical information prior to 1960, datasets for wood
harvest by FAO and urban land extent [58] in combination with assumptions of other land cover
change (e.g., forest areas, which are estimated by MODIS equipped satellites). This dataset was
chosen because it contains valuable temporal information on urbanization.
The land cover dataset was provided in form of NetCDF files at a spatial resolution of 0.5 × 0.5
degrees of latitude and longitude. Therefore, the size of each grid cell expands from 1.3475 × 10
7
m
2
to 3.088224 × 10
9
m
2
. In addition, land cover geospatial data were provided at an annual time
resolution using the WGS84 reference coordinate system. The longest record spans the years 1770–
2010, but our studied period spans from 1900 to 2010. Land cover annual maps report the percentage
of grid cell areas belonging to each of 28 land cover types, from which we focus on the urban land
Figure 16. (a) Europe and its night lights in (b) 1992, (c) 2002, (d) 2012.
Sustainability 2020,12, 7972 12 of 22
Sustainability 2020, 12, x FOR PEER REVIEW 11 of 22
Next, we explored spatial data pertaining to urbanization taking place in the past century. The
first information source examined was the spatial distribution of satellite night lights. The night lights
have been widely used as an index of the population and density of settlements [60], economic
activity [61], consumption and distribution of electricity [62], poverty and development status [63]
and human exposure to natural disasters such as floods [64]. An example showing satellite images
from city lights in Europe is shown in Figure 16, while their respective climacograms are shown in
Figure 17.
(a) (b) (c) (d)
Figure 16. (a) Europe and its night lights in (b) 1992, (c) 2002, (d) 2012.
Figure 17. Climacograms of the images of night lights of Europe.
The second information source examined was the spatial dataset on land uses. Large-scale
geospatial data, including land-cover types, were obtained from the Historical Database of the Global
Environment, HYDE 3.1 [57], of the National Centers For Environmental Information at the National
Oceanic And Atmospheric Administration (NOAA). HYDE datasets are based on Food and
Agriculture Organization of the United Nations agricultural statistics and land use (FAOSTAT) over
the period 1960–2010 [65], a variety of other historical information prior to 1960, datasets for wood
harvest by FAO and urban land extent [58] in combination with assumptions of other land cover
change (e.g., forest areas, which are estimated by MODIS equipped satellites). This dataset was
chosen because it contains valuable temporal information on urbanization.
The land cover dataset was provided in form of NetCDF files at a spatial resolution of 0.5 × 0.5
degrees of latitude and longitude. Therefore, the size of each grid cell expands from 1.3475 × 10
7
m
2
to 3.088224 × 10
9
m
2
. In addition, land cover geospatial data were provided at an annual time
resolution using the WGS84 reference coordinate system. The longest record spans the years 1770–
2010, but our studied period spans from 1900 to 2010. Land cover annual maps report the percentage
of grid cell areas belonging to each of 28 land cover types, from which we focus on the urban land
Figure 17. Climacograms of the images of night lights of Europe.
The second information source examined was the spatial dataset on land uses. Large-scale
geospatial data, including land-cover types, were obtained from the Historical Database of the Global
Environment, HYDE 3.1 [
57
], of the National Centers For Environmental Information at the National
Oceanic And Atmospheric Administration (NOAA). HYDE datasets are based on Food and Agriculture
Organization of the United Nations agricultural statistics and land use (FAOSTAT) over the period
1960–2010 [
65
], a variety of other historical information prior to 1960, datasets for wood harvest by FAO
and urban land extent [
57
] in combination with assumptions of other land cover change (e.g., forest
areas, which are estimated by MODIS equipped satellites). This dataset was chosen because it contains
valuable temporal information on urbanization.
The land cover dataset was provided in form of NetCDF files at a spatial resolution of 0.5
×
0.5
degrees of latitude and longitude. Therefore, the size of each grid cell expands from 1.3475
×
10
7
m
2
to
3.088224
×
10
9
m
2
. In addition, land cover geospatial data were provided at an annual time resolution
using the WGS84 reference coordinate system. The longest record spans the years 1770–2010, but our
studied period spans from 1900 to 2010. Land cover annual maps report the percentage of grid cell
areas belonging to each of 28 land cover types, from which we focus on the urban land cover type.
An example showing the extension of urban land cover in Europe is shown in Figure 18, while their
respective climacograms are shown in Figure 19.
Sustainability 2020, 12, x FOR PEER REVIEW 12 of 22
cover type. An example showing the extension of urban land cover in Europe is shown in Figure 18,
while their respective climacograms are shown in Figure 19.
(a) (b) (c) (d) (e)
Figure 18. Europe in the Mercator projection of urbanization in (a) 1900; (b) 1930; (c) 1960; (d) 1990;
(e) 2010.
Figure 19. Climacograms of urbanization’s images.
All studied images along with the complete climacogram analysis for Europe, Asia, America
and the globe is presented in the Supplementary Material (Figures S23–S39) and summarized in
Figure 20.
The temporal evolution of human social clustering from both information sources is presented
in Figure 20. Overall, the analyses support the case for increased human social clustering during the
20th century in all three continents, i.e., Asia, Europe and America. A few differences arise from the
comparison of the period that the information sources overlap, i.e., from the 1992 to 2010. Namely,
although urbanization appears increasing in terms of land use in America, this trend is not confirmed
by the evaluation of night lights for the same period, which appear to have slightly decreased. In
contrast, the night lights in Europe have majorly increased during this period, despite the relative
stability in the urban land use cover. These differences indicate the virtue of considering both
information sources, as night lights appear to be a better index of population density, whereas the
land use cover is more reflective of the spatial expansion of urban land uses. From this point of view,
it appears that urban expansion has been more prominent in America, whereas Europe has
experienced increased population density. Last, Asia shows consistent increases in both information
sources over the last few decades.
Figure 18.
Europe in the Mercator projection of urbanization in (
a
) 1900; (
b
) 1930; (
c
) 1960; (
d
) 1990;
(e) 2010.
Sustainability 2020,12, 7972 13 of 22
Sustainability 2020, 12, x FOR PEER REVIEW 12 of 22
cover type. An example showing the extension of urban land cover in Europe is shown in Figure 18,
while their respective climacograms are shown in Figure 19.
(a) (b) (c) (d) (e)
Figure 18. Europe in the Mercator projection of urbanization in (a) 1900; (b) 1930; (c) 1960; (d) 1990;
(e) 2010.
Figure 19. Climacograms of urbanization’s images.
All studied images along with the complete climacogram analysis for Europe, Asia, America
and the globe is presented in the Supplementary Material (Figures S23–S39) and summarized in
Figure 20.
The temporal evolution of human social clustering from both information sources is presented
in Figure 20. Overall, the analyses support the case for increased human social clustering during the
20th century in all three continents, i.e., Asia, Europe and America. A few differences arise from the
comparison of the period that the information sources overlap, i.e., from the 1992 to 2010. Namely,
although urbanization appears increasing in terms of land use in America, this trend is not confirmed
by the evaluation of night lights for the same period, which appear to have slightly decreased. In
contrast, the night lights in Europe have majorly increased during this period, despite the relative
stability in the urban land use cover. These differences indicate the virtue of considering both
information sources, as night lights appear to be a better index of population density, whereas the
land use cover is more reflective of the spatial expansion of urban land uses. From this point of view,
it appears that urban expansion has been more prominent in America, whereas Europe has
experienced increased population density. Last, Asia shows consistent increases in both information
sources over the last few decades.
Figure 19. Climacograms of urbanization’s images.
All studied images along with the complete climacogram analysis for Europe, Asia, America and
the globe is presented in the Supplementary Material (Figures S23–S39) and summarized in Figure 20.
Sustainability 2020, 12, x FOR PEER REVIEW 13 of 22
(a) (b)
Figure 20. Temporal evolution of urban clustering from evaluation of (a) city lights and (b) urban
land cover percentages.
4. Discussion
4.1. Human Social Clustering as a Means for Development and Progress
The idea of economies of scale as developed by Adam Smith [66] is that with the increase of
growth comes a decrease of the cost per unit [10]. The advantages of economies of scale have
theoretical limits, i.e., when reaching the optimal design point where the cost per additional unit
begins to increase. Economies of scale are related to scale development of infrastructures where there
are also additional limits induced due to lack of funds, technical difficulties as well as public
opposition [67] and resources accessibility. Large scales of infrastructure have risks [68] but are also
advantageous for local economies [69]. Previous work [8] has shown that changing the scale of water
infrastructures results to changes in the cost of water in agreement with the so-called “0.6 rule” in
macroeconomics [10,70,71] .
This relationship is also addressed by Wenban–Smith [72], who uses the term “density effects”
to describe the clustering trend towards concentration of population and large scales infrastructures.
For instance, in Greece we can see this clustering trend in terms of infrastructure in the construction
of large-scale dams. Other emblematic examples of large-scale projects include the controversial
“North American Water and Power Alliance” [73,74] (not constructed yet), Tehri Dam [75]
(constructed in India) and the Three Gorges Dam [76] (constructed in China).
In order to solve the problem of the optimal scale of infrastructure, multi-criteria optimization
is required. Despite the contributions of mathematicians, little progress has been made in this
engineering problem until the last half of the 20th century, when high-speed digital computers made
it possible to apply optimization techniques to large-scale structures with powerful and popular
complex optimization methods [77]. Still, it is often the case that rather than cost-benefit optimization,
political and aesthetical reasons (as the desire for creation of civilization signals), are the driving forces
behind the choice of the scale of historical infrastructures; notable examples are shown in Figure 21.
0
0.002
0.004
0.006
0.008
0.01
0.012
0.014
0.016
0.018
0.02
1992 1997 2002 2007 2012
Climacogram integral
Asia America
Europe Earth
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
1900 1930 1960 1990
Climacogram integral
Asia America
Europe Earth
Figure 20.
Temporal evolution of urban clustering from evaluation of (
a
) city lights and (
b
) urban land
cover percentages.
The temporal evolution of human social clustering from both information sources is presented in
Figure 20. Overall, the analyses support the case for increased human social clustering during the
20th century in all three continents, i.e., Asia, Europe and America. A few dierences arise from the
comparison of the period that the information sources overlap, i.e., from the 1992 to 2010. Namely,
although urbanization appears increasing in terms of land use in America, this trend is not confirmed by
the evaluation of night lights for the same period, which appear to have slightly decreased. In contrast,
the night lights in Europe have majorly increased during this period, despite the relative stability
in the urban land use cover. These dierences indicate the virtue of considering both information
sources, as night lights appear to be a better index of population density, whereas the land use cover is
more reflective of the spatial expansion of urban land uses. From this point of view, it appears that
urban expansion has been more prominent in America, whereas Europe has experienced increased
Sustainability 2020,12, 7972 14 of 22
population density. Last, Asia shows consistent increases in both information sources over the last
few decades.
4. Discussion
4.1. Human Social Clustering as a Means for Development and Progress
The idea of economies of scale as developed by Adam Smith [
66
] is that with the increase of
growth comes a decrease of the cost per unit [
10
]. The advantages of economies of scale have theoretical
limits, i.e., when reaching the optimal design point where the cost per additional unit begins to
increase. Economies of scale are related to scale development of infrastructures where there are also
additional limits induced due to lack of funds, technical diculties as well as public opposition [
67
] and
resources accessibility. Large scales of infrastructure have risks [
68
] but are also advantageous for local
economies [
69
]. Previous work [
8
] has shown that changing the scale of water infrastructures results to
changes in the cost of water in agreement with the so-called “0.6 rule” in macroeconomics [8,70,71].
This relationship is also addressed by Wenban–Smith [
72
], who uses the term “density eects” to
describe the clustering trend towards concentration of population and large scales infrastructures. For
instance, in Greece we can see this clustering trend in terms of infrastructure in the construction of
large-scale dams. Other emblematic examples of large-scale projects include the controversial “North
American Water and Power Alliance” [
73
,
74
] (not constructed yet), Tehri Dam [
75
] (constructed in
India) and the Three Gorges Dam [76] (constructed in China).
In order to solve the problem of the optimal scale of infrastructure, multi-criteria optimization
is required. Despite the contributions of mathematicians, little progress has been made in this
engineering problem until the last half of the 20th century, when high-speed digital computers made it
possible to apply optimization techniques to large-scale structures with powerful and popular complex
optimization methods [
77
]. Still, it is often the case that rather than cost-benefit optimization, political
and aesthetical reasons (as the desire for creation of civilization signals), are the driving forces behind
the choice of the scale of historical infrastructures; notable examples are shown in Figure 21.
Sustainability 2020, 12, x FOR PEER REVIEW 14 of 22
(a) (b) (c)
Figure 21. (a) The Great Pyramid of Giza 2560 BC [78] (b) Notre-Dame de Paris, towers on the west
facade 1220–1250 AD [79] (c) Eiffel Tower 1887-1889 [80].
What is common though in these large-scale projects, is the existence of an efficient state
structure able to take the relevant decisions about political and administrative mechanisms for
decisions clustering, as well as to impose and finance them. Thus, they reflect the presence of a stable
social mechanism which, according to the theory of Tomas Hobbes [81], is represented by Leviathan.
The latter metaphorically represents a central political entity that seeks to preserve law and peace by
imposing a utilitarian egoism driven by the instinct of self-preservation (conatus) and the will to
dominate, exercising absolute power only in favor of preserving social peace, i.e., the well-known
social contract. Leviathian also undertakes the protection of citizens from external and internal factors,
while also protecting citizens from the central entity itself. From this idea the Constitution originated
as a self-limitation of power. As engineering development is intertwined with social peace and
prosperity, we can assume that a form of centralized socio-political structure the likes of Leviathan is
required in order to undertake decisions about large-scale development and infrastructure projects.
Another view on the creation of large infrastructure projects through centralized social
structures is given by Aristotle [82]: “...καὶ τὸ πένητας ποιεῖν τοὺς ἀρχομένους τυραννικόν, ὅπως
μήτε φυλακὴ τρέφηται καὶ πρὸς τῷ καθ᾽ ἡμέραν ὄντες ἄσχολοι ὦσιν ἐπιβουλεύειν. παράδειγμα δὲ
τούτου αἵ τε πυραμίδες αἱ περὶ Αἴγυπτον καὶ τὰ ἀναθήματα τῶν Κυψελιδῶν καὶ τοῦ Ὀλυμπίου
οἰκοδόμησις ὑπὸ τῶν Πεισιστρατιδῶν, καὶ τῶν περὶ Σάμον ἔργα Πολυκράτεια
πάντα γὰρ ταῦτα
δύναται ταὐτόν, ἀσχολίαν καὶ πενίαν τῶν ἀρχομένων)”. English translation [83]: “And it is a device
of tyranny to make the subjects poor, so that a guard may not be kept, and also that the people being
busy with their daily affairs may not have leisure to plot against their ruler. Instances of this are the
pyramids in Egypt and the votive offerings of the Cypselids, and the building of the temple of
Olympian Zeus by the Pisistratidae and of the temples at Samos, works of Polycrates (for all these
undertakings produce the same effect, constant occupation and poverty among the subject people”.
This example highlights the mutually dependent relation between central entities and large-scale
development: the existence of the one often relies on the other.
4.2. Risks From Large-Scale Clustering
While human social clustering increases the chances for social progress and prosperity, it also
increases exposure and vulnerability to different kinds of risk. For the first time in human history,
more people live in cities than in rural areas. This rapid growth in the number of people living in
cities and urban landscapes is increasing the world’s susceptibility to natural disasters [84,85] and
other threats [86]. For instance, in the case of war, large-scale infrastructure projects are important
and common targets. Figure 22a depicts Serbian civilians, forming human shields to protect their
country's infrastructure during the NATO bombing of Yugoslavia during the Kosovo War (1999).
Large-scale infrastructures are also symbols of civilizations and this is why the World Trade Center
was a target during the 9/11/2001 attack (Figure 22b).
Figure 21.
(
a
) The Great Pyramid of Giza 2560 BC [
78
] (
b
) Notre-Dame de Paris, towers on the west
facade 1220–1250 AD [79] (c) Eiel Tower 1887–1889 [80].
What is common though in these large-scale projects, is the existence of an ecient state structure
able to take the relevant decisions about political and administrative mechanisms for decisions
clustering, as well as to impose and finance them. Thus, they reflect the presence of a stable social
mechanism which, according to the theory of Tomas Hobbes [
81
], is represented by Leviathan. The latter
metaphorically represents a central political entity that seeks to preserve law and peace by imposing a
utilitarian egoism driven by the instinct of self-preservation (conatus) and the will to dominate, exercising
absolute power only in favor of preserving social peace, i.e., the well-known social contract.Leviathian
also undertakes the protection of citizens from external and internal factors, while also protecting
Sustainability 2020,12, 7972 15 of 22
citizens from the central entity itself. From this idea the Constitution originated as a self-limitation of
power. As engineering development is intertwined with social peace and prosperity, we can assume
that a form of centralized socio-political structure the likes of Leviathan is required in order to undertake
decisions about large-scale development and infrastructure projects.
Another view on the creation of large infrastructure projects through centralized social structures
is given by Aristotle [
82
]: “...
κατ
π
έ
νητας ποιε
ν τ
οὺ
ς
ρχοµ
έ
νους τυραννικόν,
πως µ
ή
τε ϕυλακ
τρ
έ
ϕηται κα
πρ
ς τ
καθ᾿
µ
έ
ραν
ντες
σχολοι
σιν
πιβουλε
ύ
ειν.παρ
ά
δειγµα δ
το
ύ
του α
τε
πυραµ
ί
δες α
περ
ὶ Αἴ
γυπτον κα
τ
ὰ ἀ
ναθ
ή
µατα τ
ν
Κ
υψελιδ
ν κατο
ῦ ᾿Ο
λυµπ
ίο
υ
ο
κοδόµησις
π
τ
ν
Π
εισιστρατιδ
ν,κατ
ν περ
Σά
µον
ργα
Πο
λυκρ
ά
τεια
(
π
ά
ντα γρ τα
τα δύναται τατ
ó
ν
,
σχ
o
λ
ί
αν καπεν
ί
αν τ
ν
ρχ
o
µένων
)”. English translation [
83
]: “And it is a device of tyranny to make
the subjects poor, so that a guard may not be kept, and also that the people being busy with their daily
aairs may not have leisure to plot against their ruler. Instances of this are the pyramids in Egypt
and the votive oerings of the Cypselids, and the building of the temple of Olympian Zeus by the
Pisistratidae and of the temples at Samos, works of Polycrates (for all these undertakings produce the
same eect, constant occupation and poverty among the subject people)”. This example highlights the
mutually dependent relation between central entities and large-scale development: the existence of the
one often relies on the other.
4.2. Risks From Large-Scale Clustering
While human social clustering increases the chances for social progress and prosperity, it also
increases exposure and vulnerability to dierent kinds of risk. For the first time in human history,
more people live in cities than in rural areas. This rapid growth in the number of people living in
cities and urban landscapes is increasing the world’s susceptibility to natural disasters [
84
,
85
] and
other threats [
86
]. For instance, in the case of war, large-scale infrastructure projects are important and
common targets. Figure 22a depicts Serbian civilians, forming human shields to protect their country’s
infrastructure during the NATO bombing of Yugoslavia during the Kosovo War (1999). Large-scale
infrastructures are also symbols of civilizations and this is why the World Trade Center was a target
during the 9/11/2001 attack (Figure 22b).
On the other hand, modern large-scale infrastructure projects have a life of no more than 120 years
due to aging of their materials and the diculties in maintaining them [
87
]. As a simple example,
consider the two collapses of large-scale bridges that have occurred in Italy in the past few years,
causing fatalities and massive disruption of transportation [
88
,
89
]. Moreover, it is straightforward to
see how a possible failure in large-scale water-supply infrastructures upon which societies are heavily
reliant would create a vague gap in social functioning [88].
It is therefore evident that with the increase of the scale of the development along with the
planned increase of benefits comes also an increase of risks, as the concentration of goods and services
in one place makes the human communities more vulnerable to a destruction of this supply chain.
Interestingly, metaphors on the existence of a limit in the scale of human works are present in various
literature and theological works since antiquity, perhaps the most famous examples are found in the
Holy Bible. In the latter the man is regarded as the crown of God’s Creation and by the fall of man in
Original Sin, the whole Creation falls (Genesis 3.17 [
90
], St Paul, Epistle to the Romans; 8.20-22. [
91
]).
After the fall of humans, the environment became hostile and man had to do work to survive. In the
famous myth of the Babel tower, the Holy Bible explicitly communicates the notion of an upper limit
in the scale of human works (Genesis 11, Job 38:1-41 [90]).
Sustainability 2020,12, 7972 16 of 22
Sustainability 2020, 12, x FOR PEER REVIEW 15 of 22
On the other hand, modern large-scale infrastructure projects have a life of no more than 120
years due to aging of their materials and the difficulties in maintaining them [87]. As a simple
example, consider the two collapses of large-scale bridges that have occurred in Italy in the past few
years, causing fatalities and massive disruption of transportation [88,89]. Moreover, it is
straightforward to see how a possible failure in large-scale water-supply infrastructures upon which
societies are heavily reliant would create a vague gap in social functioning [90].
It is therefore evident that with the increase of the scale of the development along with the
planned increase of benefits comes also an increase of risks, as the concentration of goods and services
in one place makes the human communities more vulnerable to a destruction of this supply chain.
Interestingly, metaphors on the existence of a limit in the scale of human works are present in various
literature and theological works since antiquity, perhaps the most famous examples are found in the
Bible. In the latter the man is regarded as the crown of God’s Creation and by the fall of man in
Original Sin, the whole Creation falls [91,92]. After the fall of humans, the environment became
hostile and man had to do work to survive. In the famous myth of the Babel tower, the Bible explicitly
communicates the notion of an upper limit in the scale of human works [93,94].
(a) (b)
Figure 22. (a) Serbians protecting their country’s infrastructure from bombing as human shields [95];
(b) The north face of Two World Trade Center (south tower) immediately after being struck by United
Airlines Flight 175 [96].
Recently, due to the ongoing COVID-19 pandemic, we have been collectively reminded of how
large-scale human social clustering increases the risk of pandemics. In the developed world, the
majority of measures to mitigate the spread of the pandemic have been based on forms of social
distancing, with lock-downs being the ultimate measure. Nearly three billion people were in
quarantine in April 2020 [97]. In this respect, the Epicurean philosopher Lucretius says that if there is
no immediate risk of death, people are not afraid of death [98], but the fear of death can lead people
to make social divisions and suspend their personal growth [99]. Indeed, when people are afraid of
dying, it is common to believe that the avoidance of social contact will help them avoid danger, illness
and death altogether. This phenomenon is well documented in social fear management studies [100]
and in this context, it can also be viewed as another implicit communication of the risks of social
clustering.
5. Conclusions
It is argued herein that clustering is both a natural and a human social tendency that comes with
different qualitative consequences with scaling, i.e., the properties of large scales cannot be derived
from the ones of small scales. In these terms, as both the scales of current societies and that of
engineering projects increase, it is of paramount importance to understand both the structure of
spatial clustering and its temporal evolution. To this aim, this research develops a stochastic method
Figure 22.
(
a
) Serbians protecting their country’s infrastructure from bombing as human shields [
92
];
(
b
) The north face of Two World Trade Center (south tower) immediately after being struck by United
Airlines Flight 175 [93].
Recently, due to the ongoing COVID-19 pandemic, we have been collectively reminded of how
large-scale human social clustering increases the risk of pandemics. In the developed world, the
majority of measures to mitigate the spread of the pandemic have been based on forms of social
distancing, with lock-downs being the ultimate measure. Nearly three billion people were in quarantine
in April 2020 [
94
]. In this respect, the Epicurean philosopher Lucretius says that if there is no immediate
risk of death, people are not afraid of death [
95
], but the fear of death can lead people to make social
divisions and suspend their personal growth [
96
]. Indeed, when people are afraid of dying, it is
common to believe that the avoidance of social contact will help them avoid danger, illness and death
altogether. This phenomenon is well documented in social fear management studies [
97
] and in this
context, it can also be viewed as another implicit communication of the risks of social clustering.
5. Conclusions
It is argued herein that clustering is both a natural and a human social tendency that comes
with dierent qualitative consequences with scaling, i.e., the properties of large scales cannot be
derived from the ones of small scales. In these terms, as both the scales of current societies and that
of engineering projects increase, it is of paramount importance to understand both the structure of
spatial clustering and its temporal evolution. To this aim, this research develops a stochastic method of
general applicability for the quantification of the temporal evolution of spatial clustering as a tool to
assess, monitor and potentially predict elements of global changes.
The tool called 2D-C (2D-Climacogram) quantifies the variability of images through the variance
of the brightness intensity in grayscale. Upon a careful selection of images representing spatial
information, we can derive a quantification of clustering over time that is useful for either quantitatively
characterizing known spatial changes, as urbanization, and tracking their temporal evolution, or
even revealing spatial patterns that are less expected, i.e., pertaining to feedback loops between
anthropogenic interventions and natural variability. We present a range of applications for (a) the
natural sciences, in terms of the evolution of the universe as suggested by cosmological simulations
and of ecosystems, such as forests and lakes, and (b) for human sciences dealing with social structures,
as revealed by the evolution of worldwide cropland data, satellite images of night lights and spatial
data on urban land cover.
Our results support the concept that there is a tendency for clustering both in the natural and
anthropic world, yet this tendency is scale-dependent as beyond a certain scale it may as well be
dissolved or replaced by a structure of another quality. We have seen that in the evolution of the
universe clustering increases and decreases depending on the scale of view, and structures that have
Sustainability 2020,12, 7972 17 of 22
grown and seem at a certain scale to be merging (galaxies, clusters, super clusters, etc.), in other scales
are moving apart. In biological life clustering is related to saving of energy resources, as in in mammals,
but it is not always stable; for instance, dinosaurs disappeared. The case studies on ecosystems, namely
the Borneo and Amazon forests and the lakes in Greece, show that the clustering method oers an
eective characterization of the evolution of ecosystems revealing clustering and declustering patterns.
In many cases, the interplay of natural and human-driven variability is dicult to discern and proves
unpredictable in terms of evolution. Such a counterintuitive case is the found increase in ecosystem
variability stemming from anthropogenic interventions such as dams.
Clustering and declustering periods are apparent in nature as also revealed by our case studies,
as well as in human social structures. There are local examples of declustering, i.e., related to wars,
famines or nuclear and natural disasters, but our case studies show an overall positive clustering trend.
Specifically, in our study of long-term worldwide cropland data and London’s evolution, we have
found that the rhythm of clustering dramatically increased since the industrial revolution, whereas
urbanization followed this overall positive trend till the present time. This is in accordance with the
widespread belief that larger human clustering structures enhance eciency (e.g., through economies
of scale). Yet it is becoming increasingly evident that clustered human structures come with increased
risks as well. For instance, in the economy increasing clustering comes with increase in systemic risks,
while centralization of infrastructure and resources increases vulnerability of the population during
failure or war. In this period, the society is forced to radically reassess the clustering structures in
dierent social scales in order to tackle the risk from the COVID-19 pandemic.
Despite the vast benefits resulting from centralized social structures during the last centuries as
presented in Figures 14 and 20, at this point in time, it is tempting to consider an alternative social
distribution in space, perhaps a sparser and more decentralized one, taking example of the evolution of
natural structures that are driven by uncertainty. The COVID-19 circumstance presents an opportunity
to reconsider the trade-os resulting from our natural tendency to cluster in space. In addition, it is
an opportunity to revise the criteria for selecting the optimal scale for development, as well as the
meaning that terms such as sustainability bear under unprecedented conditions.
In any case, the answer to the question of an optimal scale of social organization and development,
is a fascinating problem that engineers among others, are urged to set and solve [
98
100
]. Homo Sapiens
survived the natural selection being a (small-scale) mammal and not a (large-scale) dinosaur. Yet
humans were ultimately able not only to adapt to new conditions but also to shape new conditions
and modify their environments through science and technology.
Supplementary Materials:
The following are available online at http://www.mdpi.com/2071-1050/12/19/7972/s1,
Figure S1. General view of the direct Cosmological Simulations of the Growth of Black Holes and Galaxies [
1
,
2
],
Figure S2. Climacograms of the Direct Cosmological Simulations of the Growth of Black Holes and Galaxies
(Figure S1), Figure S3. Closer zoom in an area of the direct Cosmological Simulations of the Growth of Black
Holes and Galaxies [
1
], Figure S4. Climacograms of the closer zoom of Direct Cosmological Simulations of the
Growth of Black Holes and Galaxies (Figure S2), Figure S5. Evolution of the universe. Millennium Simulation
Project [
3
], Figure S6. Fitting curves of composed climacograms of Millennium Simulation Project [
3
] (a) image
series of 210 mil years after B.B.; (b) image series of 1000 mil years after B.B.; (c) image series of 4700 mil years
after B.B.; (d) image series of 13,600 mil years after B.B., Figure S7. Rate of alteration of clustering through time
of image series in Figures S1, S3, S5, Figure S8. Deforestation in Borneo 1950–2005 (a) 1950; (b) 1985; (c) 2000
(d) 2005 [
4
], Figure S9. Climacograms of the deforestation in Borneo, Figure S10. Evaluation of climacograms
and rhythm of clustering in demolition of fosters’ clustering in Borneo, Greece, natural and artificial lakes (a)
overview map of the area with natural and artificial lakes in 2020; (b) layer of the map; natural and artificial lakes
2020; (c) layer of the map; lakes 2020, Figure S11. Deforestation of Amazon, creation of clustering of dry land and
urban areas inside forest [
5
], Figure S12. Climacograms of the deforestation in Amazon, Figure S13. Evaluation
of climacograms and rhythm of clustering evolution of dry-lands’ clustering in Amazon, Figure S14. Greece,
natural and artificial lakes (a) overview map of the area with natural and artificial lakes in 2020; (b) layer of the
map; natural and artificial lakes 2020; (c) layer of the map; lakes 2020., Figure S15. Evolution of water bodies in
Greece as new big dams are constructed and new artificial lakes are created, Figure S16. Climacograms of the
evolution of water bodies in Greece, Figure S17. Rate of alteration of clustering through time of water bodies in
Greece through the construction of large dams, related to GPD of Greece, Figure S18. Evolution of cropland area;
historical data from 3000 BC to AD 2000. [
6
], Figure S19. Climacograms of cropland areas, Figure S20. Evolution
of London; historical data from 1 AD to 1950 AD. [
7
], Figure S21. Climacograms. Clustering of urbanization of
Sustainability 2020,12, 7972 18 of 22
London, Figure S22. Evaluation of climacograms and rhythm of clustering (a) cropland land historical data (b)
evolution of urbanization in London area, Figure S23. (a) Mercator projection of earth and its night lights in (b)
1992; (c) 2002; (d) 2012., Figure S24. Climacograms of the images of night lights of the earth, Figure S25. Earth in
Mercator projection of urbanization in (a) 1900; (b) 1930; (c) 1960; (d) 1990; (e) 2010, Figure S26. Climacograms of
urbanization’s clustering in worldwide, Figure S27. (a) Mercator projection of Europe and its night lights in (b)
1992; (c) 2002; (d) 2012, Figure S28. Climacograms of the images of city lights of Europe, Figure S29. Europe in
Mercator projection of urbanization in (a) 1900; (b) 1930; (c) 1960; (d) 1990; (e) 2010, Figure S30. Climacograms of
urbanization’s clustering in Europe, Figure S31. (a) Mercator projection of North America and its night lights in (b)
1992; (c) 2002; (d) 2012., Figure S32. Climacograms of the images of city lights of Europ, Figure S33. North America
in Mercator projection of urbanization in (a) 1900; (b) 1930; (c) 1960; (d) 1990; (e) 2010, Figure S34. Climacograms
of urbanization’s clustering in America, Figure S35. (a) Mercator projection of Asia and its night lights in (b)
1992; (c) 2002; (d) 2012., Figure S36. Climacograms of the images of city lights of Asia, Figure S37. Asia in
Mercator projection of urbanization in (a) 1900; (b) 1930; (c) 1960; (d) 1990; (e) 2010, Figure S38. Climacograms of
urbanization’s clustering in Asia, Figure S39. Evaluation of climacograms and rhythm of clustering (a) city lights
(b) urbanization, Figure. 40. Satellite night lights of Syria taken from Reference [
59
]; (
a
) 2012; (b) 2014; (
c
) Rate of
alteration of clustering after the onset of the civil war, Figure S41. Climacograms, declustering of urbanization
in Syria.
Author Contributions:
Conceptualization, G.-F.S., P.D.; methodology, G.-F.S., P.D. and D.K.; software, P.D. and
S.S.; validation, G.-F.S.; formal analysis, G.-F.S. and S.S.; investigation, G.-F.S.; resources, S.S.; data curation, G.-F.S.
and S.S.; writing—original draft preparation, G.-F.S., T.I. and S.S.; writing—review and editing, G.-F.S., T.I. and
D.K.; visualization, G.-F.S.; supervision, D.K.; project administration, G.-F.S.; funding acquisition, none. All
authors have read and agreed to the published version of the manuscript.
Funding: This research received no external funding.
Acknowledgments:
We thank the editors Kevin Cianfaglione, DoruB
ă
n
ă
duc, assistant editors of Sustainability-MDPI,
as well as three anonymous reviewers for their comments that helped improve and enrich the manuscript. In
particular, we appreciate the third reviewer’s enthusiastic evaluation of our paper. We would also like to thank
Kimon Hadjibiros for inspiring philosophical discussions and Dionysios Nikolopoulos for his encouraging reaction
to an initial presentation of the paper’s concept.
Conflicts of Interest: The authors declare no conflict of interest.
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... This gave them the ability to cluster in smaller spaces such as villages and, later, cities. The increase in clustering was a stride of civilization [2,3], but cities always depended on external resources (e.g., in antiquity, Athens imported wheat from the area of the Black Sea [4,5]). ...
... Partitioning is a method of protection and can be applied to many different threats such as viruses (social distancing), wars, and wildfires [2,63]. Using satellite images and publicly available data, we evaluate by Climacogram Integral the evolution of spatial clustering in Europe (1990-2010) using Hurst-Kolmogorov dynamics [2,[64][65][66][67][68][69][70][71]. ...
... Partitioning is a method of protection and can be applied to many different threats such as viruses (social distancing), wars, and wildfires [2,63]. Using satellite images and publicly available data, we evaluate by Climacogram Integral the evolution of spatial clustering in Europe (1990-2010) using Hurst-Kolmogorov dynamics [2,[64][65][66][67][68][69][70][71]. Urbanization is reflected in the increasing trend of cities' clustering, which we have observe lately. ...
Article
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The formation of societies is based on the dynamics of spatial clustering, which optimizes economies of scale in the management of the water–energy–food (WEF) nexus. Energy and food are determinant measures of prosperity. Using the WEF nexus as an indicator, we evaluate the social impacts of the current (2022) conflict and in particular the economic sanctions on Russia. As Russia and Ukraine are major global suppliers of energy sources, food, and fertilizers, new threats arise by their limitations and the rally of prices. By analyzing related data, we show the dramatic effects on society, and we note that cities, which depend on a wider area for energy and food supplies, are extremely vulnerable. This problem was substantially worsened due to the large-scale urbanization in recent decades, which increased the distance from food sources. We conjecture that the Western elites’ decision to sanction Russia dramatically transformed the global WEF equilibrium, which could probably lead to the collapse of social cohesion.
... The 1D clustering behavior has been identified in many scientific fields (see reviews in [7,[15][16][17]). The 2D spatial clustering behavior has also been explored in many fields such as hydrology (e.g., [18][19][20], and references therein), biology and ecosystems (e.g., [21,22]), life sciences (e.g., [23][24][25][26]), networks (e.g., [27][28][29]), urban structures (e.g., [30,31]), rock formation (e.g., [32]), turbulence (e.g., [7,33]), art (e.g., [34][35][36]), landscape analysis (e.g., [37,38]), simulated evolution of the universe [39] and many others (e.g., [40]). A unified approach for the quantification of the 2D spatio-temporal clustering in terms of variability in the scale domain (instead of in the common lag and frequency domains) can be Encyclopedia 2021, 1, FOR PEER REVIEW 2 of high-order moments in a vast range of scales [10,11], affecting both the intermittent (fractal) behavior in small scales [12] and the dependence in extremes [13]. ...
... The 1D clustering behavior has been identified in many scientific fields (see reviews in [7,[15][16][17]). The 2D spatial clustering behavior has also been explored in many fields such as hydrology (e.g., [18][19][20], and references therein), biology and ecosystems (e.g., [21,22]), life sciences (e.g., [23][24][25][26]), networks (e.g., [27][28][29]), urban structures (e.g., [30,31]), rock formation (e.g., [32]), turbulence (e.g., [7,33]), art (e.g., [34][35][36]), landscape analysis (e.g., [37,38]), simulated evolution of the universe [39] and many others (e.g., [40]). A unified approach for the quantification of the 2D spatio-temporal clustering in terms of variability in the scale domain (instead of in the common lag and frequency domains) can be Hurst-Kolmogorov (HK) dynamics present in the annual minimum water level of the Nile River as a result of the perpetual change of Earth's climate, and as compared to a roulette timeseries resembling a white noise process. ...
... The 1D clustering behavior has been identified in many scientific fields (see reviews in [7,[15][16][17]). The 2D spatial clustering behavior has also been explored in many fields such as hydrology (e.g., [18][19][20], and references therein), biology and ecosystems (e.g., [21,22]), life sciences (e.g., [23][24][25][26]), networks (e.g., [27][28][29]), urban structures (e.g., [30,31]), rock formation (e.g., [32]), turbulence (e.g., [7,33]), art (e.g., [34][35][36]), landscape analysis (e.g., [37,38]), simulated evolution of the universe [39] and many others (e.g., [40]). A unified approach for the quantification of the 2D spatio-temporal clustering in terms of variability in the scale domain (instead of in the common lag and frequency domains) can be found in the applications of the current entry, where a stochastic methodology is presented that quantifies clustering in 2D spatial fields by analyzing the spatial structures over time, and by exploring how the HK dynamics highly increase the induced uncertainty in terms of spatio-temporal variability in the scale domain. ...
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The stochastic analysis in the scale domain (instead of the traditional lag or frequency domains) is introduced as a robust means to identify, model and simulate the Hurst–Kolmogorov (HK) dynamics, ranging from small (fractal) to large scales exhibiting the clustering behavior (else known as the Hurst phenomenon or long-range dependence). The HK clustering is an attribute of a multidimensional (1D, 2D, etc.) spatio-temporal stationary stochastic process with an arbitrary marginal distribution function, and a fractal behavior on small spatio-temporal scales of the dependence structure and a power-type on large scales, yielding a high probability of low- or high-magnitude events to group together in space and time. This behavior is preferably analyzed through the second-order statistics, and in the scale domain, by the stochastic metric of the climacogram, i.e., the variance of the averaged spatio-temporal process vs. spatio-temporal scale.
... In prehistory, humans relied on energy and water to transition from hunter-gatherers to farmers, and this gave them the ability to cluster in smaller spaces like cities [1] and the increase of clustering gives rise to civilization [66]. Today, humanity is facing a major challenge: the rapidly growing demand for WEF. ...
... Notably, the optimization of WEF nexus management is already part of the evolution process of Homo sapiens. Related papers have given an overview of the relationship, through the evolution process, of Homo sapiens with items such as:  water and food consumption [66],  walking on two feet which was an energy-saving step [70], and  the function of the brain, which is more energy efficient than in animals [71]. ...
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Water, energy, land, and food are vital elements with multiple interactions. In this context, the concept of a water-energy-food (WEF) nexus was manifested as a natural resource management approach, aiming at promoting sustainable development at the international, national, or local level and eliminating the negative effects that result from the use of each of the four resources against the other three. At the same time, the transition to green energy through the application of renewable energy technologies is changing and perplexing the relationships between the constituent elements of the nexus, introducing new conflicts, particularly related to land use for energy production vs. food. Specifically, one of the most widespread "green" technologies is photovoltaic (PV) solar energy, now being the third foremost renewable energy source in terms of global installed capacity. However, the growing development of PV systems results in ever expanding occupation of agricultural lands, which are most advantageous for siting PV parks. Using as study area the Thessaly Plain, the largest agricultural area in Greece, we investigate the relationship between photovoltaic power plant development and food production in an attempt to reveal both their conflicts and their synergies.
... At the beginning, humans survived, perpetuated and spread as hunter gatherers, dominating the environment, reaching a relative equilibrium [56] and displaying remarkable resilience [57]. The possibility of human clustering [58,59] was very small, since man needed large areas to meet nutritional needs [60]. The great step toward civilization was primarily due to the capability of human clustering through language and technology. ...
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The pursuit of wealth has been a basic occupation of humans; as it turns out, wealth increases life expectancy. Analyzing global data, we show that money, probably connected with medical care, increase life expectancy. However, the base of real wealth is access to the Water–Energy–Food nexus, and the access to this also increases life expectancy. The first objective of this study was to compare the present values of wealth with antiquity, and we showed that about 1.4 billion people live in the present under the average lower wages of antiquity. As a case study, we analyze the construction of the Hadrianic aqueduct. We present a detailed description of the construction and the used methods, and we identify the total requirement of labor–time. Then, we investigate the wages of various occupations in the first century AD. The second objective of this study was the estimation of the total cost of daily wages for the construction of the project and the effect of the aqueduct on Athenians’ quality of life. Finally, we show that, today, about two billion people live with less available water than Athenians had with the Hadrianic aqueduct in the second century A.D.
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Living organisms pass through life seeking prosperity in a materialistic world. There are different meanings of prosperity. Some people think that it is measured in money, others relate it to pleasure and life satisfaction, while others link it to spirituality. However, it could be argued that the basic human needs related to the Water, Energy and Food (WEF) compose a nexus not only necessary for the survival of humans, but able to explain their prosperity as well. Unfortunately, decision-making in modern world is largely driven by economic aspects and monetarist policies. Koutsoyiannis (personal communication) notes that water, energy and food are not derived by money; rather money and economic growth derives from the availability and the access to water, energy and food. In this thesis, we study critical issues of prosperity rationally, using publicly available data, historical evidences and stochastic tools. The studied issues are based on the WEF nexus but extend to various other societal, environmental and cultural aspects of human life in societies, ranging from social stratification and urban clustering, to the aesthetic quality of surrounding environment.
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Landscape impacts associated with aesthetics have been a persistent cause of opposition against renewable energy projects. However, the current uncertainty over the spatial extents and the rationality of reported impacts impedes the development of optimal strategies for their mitigation. In this paper, a typology of landscape impacts is formed for hydroelectric, wind and solar energy through the review of three metrics that have been used extensively for impact-assessment: land use, visibility and public perception. Additionally, a generic landscape-impact ranking is formed