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Complex Adaptive Systems (CAS) is a framework for studying, explaining, and understanding systems of agents that collectively combine to form emergent, global level properties. These agents can be nearly anything, from ants or bees, to brain cells, to water particles in a weather pattern, to groups of cars or people in a city or town. These agents produce emergent patterns via correlated feedbacks throughout the system, feedbacks that create and fortify a basin of attraction: a persistent pattern of behavior that itself is outside of equilibrium. There is also an ever-growing understanding that similar features in complex systems across a diversity of domains may indicate similar fundamental principles at work, and as such there is often utility in using the key features of one system to gain insight into the workings of seemingly distinct fields. Here we also include a brief review of multiple models that attempt to do exactly this, including some of our previous work. Though there is not complete agreement on all aspects and definitions in this field, this introduction also summarizes our understanding of what defines a CAS, including the concepts of complexity, agents, adaptation, feedbacks, emergence, and self-organization; and places this definition and its key features in a historical context. Finally we briefly discuss two of the common biases often found that the tools of CAS can help counteract: the hierarchical bias, assuming a strong top-down organization; and the complexity bias, the tendency to assign complicated features to agents that turn out to be quite simple.
The Fundamentals of Complex Adaptive
Ted Carmichael and Mirsad Hadˇ
Abstract Complex Adaptive Systems (CAS) is a framework for studying, explain-
ing, and understanding systems of agents that collectively combine to form emer-
gent, global level properties. These agents can be nearly anything, from ants or bees,
to brain cells, to water particles in a weather pattern, to groups of cars or people in
a city or town. These agents produce emergent patterns via correlated feedbacks
throughout the system, feedback that create and fortify a basin of attraction: a per-
sistent pattern of behavior that itself is outside of equilibrium.
There is also an ever-growing understanding that similar features in complex sys-
tems across a diversity of domains may indicate similar fundamental principles at
work, and as such there is often utility in using the key features of one system to
gain insight into the workings of seemingly distinct fields. Here we also include a
brief review of multiple models that attempt to do exactly this, including some of
our previous work. Though there is not complete agreement on all aspects and def-
initions in this field, this introduction also summarizes our understanding of what
defines a CAS, including the concepts of complexity, agents, adaptation, feedbacks,
emergence, and self-organization; and places this definition and its key features in a
historical context. Finally we briefly discuss two of the common biases often found
that the tools of CAS can help counteract: the hierarchical bias, assuming a strong
top-down organization; and the complexity bias, the tendency to assign complicated
features to agents that turn out to be quite simple.
Ted Carmichael
University of North Carolina at Charlotte, Department of Software and Information Systems, 9201
University City Blvd, Charlotte, NC 28223; and
TutorGen, Inc., 1037 S Ft Thomas Ave, Fort Thomas, KY 41075. e-mail:
Mirsad Hadˇ
University of North Carolina at Charlotte, Department of Software and Information Systems, 9201
University City Blvd, Charlotte, NC 28223 e-mail:
2 Ted Carmichael and Mirsad Hadˇ
1 Overview
Most interesting collective phenomena in natural and social systems can be de-
scribed as having stable and persistent states, often outside of equilibrium. The term
basin of attraction has been used to describe such systems, capturing the idea of
correlated feedbacks among the agents of a system that create these identifiable and
distinct patterns. These systems are so defined because they are resilient in the face
of external forces, but can nevertheless also exhibit tipping points: situations where
the stable system finally crosses some threshold, and begins a rapid transition to a
new state. These thresholds can be characterized as a qualitative change in system
characteristics: a change in sign or abrupt change in magnitude (either enduring or
a spike) in the first or second derivative of a system variable.
Threshold effects are found all around us. In economics, this could be movement
from a bull market to a bear market; in sociology, it could be the spread of political
dissent, culminating in rebellion; in biology, the immune system response to infec-
tion or disease as the body moves from sickness to health. Companies, societies,
markets, or even humans represent such persistent states that can change rapidly at
any time. Both endogenous and exogenous feedbacks can cause sudden, non-linear
shifts in system behavior, ensuring that the future of these systems are often un-
known and challenging. How do events unfold? When do they take hold? Why do
some initial events cause an avalanche of change while others do not? What char-
acterizes system stability and resilience? What are the thresholds that differentiate a
sea change from negligible variations?
Complex Adaptive Systems (CAS) has proven to be a powerful framework for
exploring thresholds and resilience, and other related phenomena. As the name im-
plies, a CAS is a system of agents that interact among themselves and/or their en-
vironment, such that even relatively simple agents with simple rules of behavior
can produce complex, emergent behavior. The key to CAS is that the system-level
properties generally cannot be understood, or often even defined, at the level of the
individual agent description. Therefore, these systems must be studied holistically,
as the sum of the agents and their interactions.
1.1 Defining CAS
We characterize a general CAS model as having a significant number of self-similar
agents that:
Utilize one or more levels of feedback;
Exhibit emergent properties and self-organization;
Produce non-linear dynamic behavior.
The CAS framework can be used to describe systems that encompass phenomena
across many diverse environments and a wide range of disciplines. These systems
are present at all scales of inquiry: from the movement of markets and economies to
The Fundamentals of Complex Adaptive Systems 3
individual knowledge acquisition; from large-scale social interaction to small-scale
cellular behavior. Advances in modeling and computing technology have not only
led to a deeper understanding of complex systems in many areas but have also raised
the possibility that similar fundamental principles may be at work across a wide va-
riety of domains. This idea has led to several multidisciplinary conferences forming
to allow the sharing of ideas across domains, including the annual Swarmfest meet-
ing, and The Association for the Advancement of Artificial Intelligence (AAAI)
CAS Fall Symposia series, from where the papers in this volume are drawn.
The overriding goal for these conferences is to create synergy and build connec-
tions amongst domain-specific experts. Often, complex systems from two distinct
fields may seem different on the surface, but have quite similar underlying dynam-
ics. We hypothesize that by modeling complex systems from many different areas,
we can start to find the principles that show common causes and common effects
across domains. In this way, the known causes and mechanisms in one domain are
used to gain insight into the controlling properties of similar effects in other do-
mains. As Neil Johnson writes:
In particular, the connections between such systems have not been properly explored
particularly between systems taken from different disciplines such as biology and sociology.
Indeed it is fascinating to see if any insight gained from having partially understood one
system, say from biology, can help us in a completely different discipline, say economics
[14, p. 16].
Put another way, Epstein writes:
Generality, while a commendable impulse, is not of paramount concern to agent-based mod-
elers at this point [10, p. 1602].
And so we believe that by bringing these researchers together, who study different
fields but use the same tools and techniques of CAS and Agent-based Modeling
(ABM), we can overcome the natural tendency of scholars to work only within
their own silos, and encourage fruitful and cross-disciplinary collaborations that
successfully draw generalities across domains.
1.2 Common Models Across Diverse Domains
As an illustrative example consider the model found in Midgley, Marks, and Kun-
chamwar [17], one of numerous examples of using ABM to implement a CAS
framework to further understanding of the dynamics found within a particular sys-
tem. In this work, the authors construct a model that aims to reproduce a typical
market structure by utilizing the properties of a supermarket setting. Their model
incorporates three types of agents: consumers, retailers, and manufacturers. They
have chosen ABM over more traditional methods of model construction that use
game theory or analytical equations of system dynamics, due to the power and flex-
ibility of CAS:
4 Ted Carmichael and Mirsad Hadˇ
[O]ne can more easily incorporate the existing knowledge about the nature of human-
decision-making processes into AB models than into analytical equations. [...] AB models
allow a flexibility of representation that is not present in more traditional approaches.
But Midgley et al.’s model was not designed with general applicability in mind.
It may be that some of the agent attributes could reasonably be applied to other
domains. For example, chance of observing a store promotion might be a stand-in
for vision;number of best promotions remembered may be generalized as memory;
and perhaps satisfaction threshold for an agent could represent any state-change
threshold for any agent. But it has not been explicitly explored how these transla-
tions may be realized, or to what advantage, in a different system. Other attributes,
such as range of advertising levels or quarterly increment/decrement to mark-up,
may not have any obvious analogues. Further, the rules governing calculations that
utilize these attributes also suffer a lack of generalizability or an explicit method for
applying these rules to a new domain.
In [22] the authors present a more general economic model, utilizing only two
agents: buyers and sellers. While this work is intended to demonstrate the utility of
ABM in this context, it is quite clear that these agents may be easily applicable to
many types of markets. However, as with [17], there is no discussion or representa-
tion of this models applicability to systems that are outside of economics.
Examples from other domains also follow this common pattern. Vries and Bies-
meijer have created an ABM of honeybee foraging [7], which they expanded upon
in [8]. While this work is intended to utilize enough flexibility to represent a broad
range of variable values found in real-world honeybee colonies, it does not pur-
port to show general adaptability to other fields. Similarly, ABM has been used to
develop sophisticated tools for the study of traffic flow under a wide spectrum of
environmental factors, such as weather, infrastructure, and changing demographics.
[11] describes one such system; but again, limited to only a single domain.
There have also been examples of ideas or concepts of CAS taken from one do-
main and applied to one or more others. Schellings classic model on segregation [20]
is an example of a fundamental property, one that may be readily applied to many
systems, informing models found in sociology, biology, or economics. Flocking be-
havior has been studied in birds, fish, and crowds of people, and simple analogies
between these diverse systems can be drawn [21]. Also, the collective intelligence
of ants for determining the shortest path has proven to be useful in the engineer-
ing of decentralized flow control, such as in computer networks. In general, these
examples illustrate how one system can inform study of another: either by drawing
comparisons from one model to another, or by using certain properties found in one
model to inform the construction of a second model.
In furthering this idea our prior work has explored using a single CAS tool to
replicate key properties of complex systems as found in multiple domains: a single
model with multiple applications. This model was developed and used to simulate
the growth of cancer and the immune system response; and then used to show sim-
ilarities in the growth of a social contagion effect in a polity, and the government
response to this growing unrest [5]. We noticed that both of these systems exhibited
properties of predators and prey, and so we adapted the model to also simulate a gen-
The Fundamentals of Complex Adaptive Systems 5
eralized predator-prey system, replicating key phenomena found in the ecosystem
literature such as Gauses Law, the stepped pattern of biomass accrual, the Compet-
itive Exclusion Principle [3]. With this model we also discovered some surprising
limits on the Red Queen Effect: the idea that competitive populations will perform
an arms race to continually outstrip the other group [4].
This endeavor is similar in scope to the work of Nicolis and Prigongine [18].
As described by [21], they were attempting to develop a rigorous theory of self-
organizing behavior, and they were successful in showing that mathematical equa-
tions used to describe chemical reactions could also apply to the cyclical dynamics
of a predator-prey model. However, their approach did not use a stochastic ABM
method; rather, it relied on idealized equations which though useful are diffi-
cult for representing a diversity of agents and agent-attributes.
Our generalizability approach in [5] is most similar to that used previously by
Axelrod et al. [1]. In this work, a model of political state-level alliances during
World War II was successfully applied to an economics system of company-level
alliances. In the political model there are five attributes such as shared religion
or border disputes that were used as either attractors or repulsors in a pair-wise
calculation of affinity across 17 countries. These affinity calculations 65,536 in
total would then determine the alliances of each country (subsequently labeled
either Allies or Axis). No matter what the initial conditions, only one of two final
configurations appeared each time, one of which was correct for all 17 countries
save one.
This same model was then applied to the case of eight computer companies
choosing which coalition to support between two competing versions of the UNIX
operating system. This application used the same theory as that for the political
model, simply adapting the attributes and relative sizes of each actor, and the model
successfully predicted the real-world strategic alliances that the computer compa-
nies formed.
The primary difficulty with [1] is that there are so few agents in each system: only
seventeen for the political case and eight for the business case. This limitation opens
up the model to criticism, in terms of agent attributes that could, perhaps, be easily
calibrated to predict a known result. Also, this system is not intended to simulate the
machinations of the countries or the companies over time; rather, it merely searches
for a single end state. Further, it is unclear how a set of these weights in one domain
political alliances would help inform similar weights in another domain, such
as corporate alliances.
Nevertheless, the strength of their work is that the models interactions are trans-
latable from one domain to another, particularly regarding the underlying theory
used in both cases. Such cross-disciplinary applicability is the overarching goal
of the symposia and conferences that we have organized over the years, includ-
ing through the AAAI, and the annual Swarmfest meetings that are represented in
this volume. Ultimately it would be more interesting and, perhaps, more useful if
such trans-disciplinary models displayed similar characteristics and outputs not just
at one moment in time, but over complete model runs, so that it is not just end-states
that show similarities, but also the dynamics that get you there. This is a much more
6 Ted Carmichael and Mirsad Hadˇ
difficult goal to reach, of course, but perhaps also more significant and therefore
more worthwhile to pursue.
2 Properties of Complex Adaptive Systems
This section looks at some of the earliest work used to formulate the paradigm of
CAS and touches on the fundamental properties and key characteristics that define
this paradigm.
2.1 Historical Context
In the 1960s researchers were trying to understand better the dynamics of slime
mold: in particular, there was a persistent mystery in how it could transition between
its active and its dormant states [15]. Biologists had long known about slime molds
strange behavior, acting as a single organism under some conditions, and devolving
into individual cells under other conditions. They knew that a chemical acrasin was
somehow involved, and speculated that there were pacemaker cells which would
produce an acrasin and thereby attracted the other cells to it. Years of study were
conducted in the vain search for these pacemakers.
In the late 1960s a physicist and a mathematician (Evelyn Keller and Lee Segal)
came across a paper by Alan Turing that described what he termed morphogenesis:
the idea that organisms can form great complexity from simple roots. Published in
1952, it was one of the last papers he produced, and in it, he described a mathe-
matical model whereby simple organisms, following just a few simple rules, could
produce strikingly complex patterns [23].
Keller and Segal took the ideas in Turings paper and developed the mathematics
to describe a system of slime mold, demonstrating that it is not necessary to account
for pacemaker cells in such a model. Rather, all that was required to reproduce the
properties of the system were two rules: that each cell simultaneously produces,
and is attracted to, an acrasin. These two simple rules were sufficient to account for
the molds strange behavior, and demonstrated how this collective interaction could
allow numerous individual cells to form a multi-cellular organism, one that could
move about its environment and act as a single living being. A third rule, that the
cells produce the acrasin under certain environmental conditions, was sufficient to
explain the transition from a dormant state to an active one.
In this way, the description of a slime-mold model exhibits all the classic proper-
ties of a CAS: the agents (cells) of the slime-mold affect each other via the feedback
mechanisms inherent in the two rules; they also react to the influence of the chang-
ing environment, which is sufficient to activate these two rules; once activated, the
cells self-organize as an emergent property of this system; and finally, the threshold
The Fundamentals of Complex Adaptive Systems 7
change in behavior of the slime-mold organism represents the non-linear dynamics
necessary to adapt to new environmental conditions.
This re-framing of the slime-mold behavior is indicative of a systems-level ap-
proach to studying complex phenomena. This framework was recognized as a new
way to approach system-level phenomena in many other fields, such as the clas-
sic invisible hand that governs the marketplace, as found in the work of economist
Adam Smith; or the contagion effect, found in social theory as well as epidemiology
studies; or the study of traffic patterns and the movement of crowds. The subsequent
founding of the Santa Fe Institute in 1984 by Murray Gell-Mann, a physicist; John
Holland, a biologist; and others, is seen by many as the beginning of CAS as an
explicit field of study [24]. They recognized the multidisciplinary nature of these
phenomena, and thus brought together scholars from many different areas to begin
the process of applying CAS to a wide variety of research questions.
2.2 Complexity
There is not yet a single, agreed-upon theory that describes complexity or a complex
system equally for every situation. As with many things, it is often a matter of degree
or perspective, rather than clear distinction, as to what is complex and what is not.
However, we can distinguish some key characteristics of a complex system for our
purposes here.
The most general distinction we use refers to Warren Weavers division of com-
plexity into two types: disorganized complexity and organized complexity [25]. Dis-
organized complexity refers to a system of many even millions of parts that interact
at random, producing aggregate effects that can easily be described using probabil-
ity and statistical methods. The example he gives is that of a very large billiard table
with millions of balls rolling in different directions, colliding with each other and
with the walls. Even though the path of a single ball may be erratic, or even un-
known, the system itself has measurable average properties. Clearly, there is feed-
back in such a system: one billiard ball strikes another, and then that ball can bounce
around and strike back. But this does not suffice. There is something missing in this
system, without which it cannot produce self-organizing behavior.
What we are concerned with here, then, is organized complexity. Organized com-
plexity refers to a system with a sizable number of agents which have correlated in-
teractions. And since these interactions are correlated, they can produce emergent,
global-level properties for the system as a whole.
An average quantity alone is not an emergent feature. Yet statistical quantities, which define
properties of an aggregation, can be regarded as simple emergent properties if they depend
on a relation of the particles to each other, i.e., if they do not make sense for a single particle
[12, p. 8].
Correlation among the interactions in such a system implies two things: 1) that
the agents of the system exhibit feedback mechanisms; and 2) that these feedback
8 Ted Carmichael and Mirsad Hadˇ
mechanisms are, by definition, endogenous to the system itself. In this way, the
agents affect each other in a correlated manner.
2.3 Agents
The term agent tends to be an overloaded one. Some researchers, therefore, may use
an alternative, such as particle, to describe the individual objects of a complex sys-
tem [16]. While logically sound in the way Kennedy et al. present the term, it doesnt
seem to capture the autonomy, or intent, of many agents; particularly those found in
social systems. Thus we use the more conventional term agent in our description.
But we distinguish between the somewhat overlapping conceptions of agents found
in CAS relative to those generally described in a Multi-agent System (MAS) [27].
CAS agents possess simple rules and attributes; are largely autonomous with only
local knowledge; and, as constituent parts of a larger system, are easily replaced by
similar agents without disrupting the emergent features of that system. In contrast,
MAS agents tend to be more autonomous and intelligent, more complicated, and
fewer in number. MAS agents also tend to fall into a strict hierarchy, whereas CAS
agents are easily replaced or switched around. Contrast all the individual parts of a
car with, say, a colony of bees. Each bee is easily replaced with another, whereas
each part of a car has a strict function and placement.
Finally, emergence in most MAS models is usually mentioned only as something
to be avoided if possible, rather than as an inherent, key property of the system. In
CAS, emergence is considered a feature, not a bug.
Put another way, building a car is complicated. The agents are specific, diverse,
and fall into a strict hierarchy. Driving a car is complex: dynamic and ever-changing,
with multiple levels of feedback and a loose hierarchy of replaceable agents.
In our work we also consider CAS agents to be self-similar, to use a term com-
mon in the literature; i.e., the agents are largely homogeneous. It is worth noting
that many published works refer to these not as homogeneous agents, but as het-
erogeneous agents, such as in Epstein [9, pp. 5-6]. We believe the discrepancy is
simply a difference in emphasis. As Epstein uses the term heterogeneous, he is re-
ferring to a differentiation regarding the agent attribute-values, not the agent spec-
ifications themselves. That is, his heterogeneous agents have a range of values for
their attributes, not a range of attributes. While other authors may call such agents
homogeneous due to their similarity, it is useful to understand that these authors are
talking about the same thing. To avoid ambiguity, we use the term self-similar, while
also recognizing that the agents of a complex system can be different but not too
different in terms of the rules and attributes that relate to the emergent property
in question.
These differences across agents do matter, in their variety, because a particular
emergent property depends upon a degree of self-similarity within the system. Con-
sider a simple model of traffic flow as an example, with the agents as cars moving
along a highway. Each agent has two rules: slow down if the car ahead is too close,
The Fundamentals of Complex Adaptive Systems 9
and speed up if it is too far away. Under some conditions, a wave-like pattern can
emerge across the ebb and flow of the cars, as one car slows, causing the next in line
to slow, also. In simulations, this can occur whether the rules for slowing down and
speeding up are exactly the same across all cars, or if there is some slight variation
for the activation of each rule (i.e., if they are heterogeneous in attribute-values).
But if some agents have rules that allow them to stop completely, or crash, or drive
off the road if they are too heterogeneous in their attributes then this chaotic
behavior would disrupt the emergent patterns of traffic. The system breaks down if
the agents diverge too far in their rules and attributes.
Similarly, if the flocking example found in [26] were adjusted so that some agents
have wildly different attributes, then flocking may not be a reachable state for the
system. If there is no correlated feedback among the agents, then an emergent prop-
erty is impossible.
The degree to which agent must be similar depends upon the characteristics of
the model being studied; specifically, it depends on the emergent behavior that is
of interest. For example, the agents in the traffic pattern may be made much more
complex, with many more attributes, than two simple rules of when to speed up and
when to slow down. Each agents perceptions, disposition, reactive ability, and etc.,
could be included in the specifications. And many other agent attributes besides. But
note that these attributes, and many more, only matter to the degree that they relate to
the two conditions that produce the emergent behavior. No matter how complex the
calculations that take into account perceptions, disposition, reaction times, and so
forth, they ultimately determine only an expression of the two rules: when to speed
up and when to slow down. The agents may be described as quite heterogeneous
across all these attribute values, but they must be self-similar enough to produce an
emergent traffic pattern that can be analyzed and compared to real-world data.
2.4 Agent-level vs. System-level Adaptation
Agent-level adaptation implies some sort of fitness function or selection criteria
for agents, based on their attribute-values. This further implies some difference or
capacity for change among the agents attribute-values; and more than just superfi-
cial differences, but rather functional and consequential heterogeneity. Agent-level
adaptation becomes hard to distinguish under certain conditions, however. To illus-
trate the potential difficulty, imagine an economics model where agents sell a certain
good at a certain price. The agents each have a rule that states: sell product X for no
less than Y units of money. On one level, these two agents are exactly the same, in
that their internal rules are the same, even if one agents current state for the value
of Y is 10 dollars while another agent has his Y set to 11 dollars. The difference
between the first and second agent is not the difference in rules or attributes, but in
one attribute value. In this sense, these agents are still homogeneous, because they
have the same type of rules, and they apply these rules in the same way. In another
10 Ted Carmichael and Mirsad Hadˇ
but very real sense, these agents are heterogeneous, adapting individually as
each adjusts his price point for maximum efficiency.
This sort of change in the agents state can be termed learning, or adaptation,
or even evolution: all words that mean essentially the same thing, but fall along
an implied continuum of persistence and complexity. Learning is the easiest, and
fastest to change, while evolution tends to be on longer time-scales, and is more
permanent. Thus, our hypothesized economic agents may learn a new price-point
for selling, and this price point may be updated daily. Or, some of these agents may
adapt, changing their internal algorithms used to update this price point. Or going
even further the agents may evolve, perhaps changing their modes of behavior so
that they not only sell product X, but can buy it as well.
In contrast to agent-level adaptation, system-level adaptation is when a group of
agents changes in a correlated way, reacting holistically to the environment. In gen-
eral, we label system-level adaptation as correlated changes in the attribute-values
among a large group of connected agents. Agent-level adaptation, then, is a more
substantial change in an individual agent, such as changes in the set of agent rules or
attributes. And thus system-level adaptation could be represented by a flock of birds
that sees a predator. The flock may shift and split apart as the individual birds try to
avoid the predator, and these birds influence their neighbors to change direction as
well. Even though no individual bird has changed how it reacts to seeing a predator
i.e., they haven’t adapted or evolved the flock itself can adapt to avoid the
danger. It is this system-level adaptation that gives CAS its power: collectives re-
acting intelligently to the environment, with complex dynamics and versatility, even
though they are comprised of very simple agents.
2.5 Feedbacks
Feedback, simply defined, means that the outputs of a system at time taffect the
inputs of that system at time t+1. As the agents in a complex system interact, the
results of some interactions may influence future interactions. It is this influence
that represents the feedback within the system itself. In the previously mentioned
model of traffic patterns along a highway, one car that slows down in response to
the car in front of it may then produce a similar effect in the next car in line. This
action/response that can easily produce a wave of congestion along the highway is
due to feedback between the cars, from one to the next in line. It is worth pointing
out that the term wave is apt in this case, as it describes a pattern of behavior across
multiple agents, much like a wave in the ocean, even though the agents participating
in the pattern change over time. This matches well with how Holland and others
have described emergence in complex systems:
Emergent phenomena in generated systems are, typically, persistent patterns with changing
components [13, p. 225].
The Fundamentals of Complex Adaptive Systems 11
Note also the distinction between this organized feedback as compared to the
disorganized complexity of our billiard table. While it is true that one collision be-
tween two balls alters the course of future collisions, it does not affect the course of
future collisions persistently; that is, if one colliding ball happens to bounce to the
north, it does not mean that the next ball struck will also bounce northward.
Relationships in these systems are mutual: you influence your neighbors, and your neigh-
bors influence you. All emergent systems are built out of this kind of feedback [15, p. 120].
The key point here is that such reciprocal influence among neighbors is more
significant when it creates measurable, global properties. The action/reaction pat-
terns represent the correlations within the system that make up these global proper-
ties. While our traffic pattern example may have measurable statistical properties
such as how many cars traverse the highway in a given day these measurements
do not fully capture the wave-like behavior of the system. It is by identifying the
correlated feedback that we find a richer, and therefore more interesting, description
of the system.
2.6 Endogenous vs. Exogenous Factors
One may want to consider the first action that sets the pattern in motion is it
an endogenous or exogenous instigator? While the resultant pattern is certainly en-
dogenous to the system, the initiation of that pattern may be either. It can sometimes
be difficult to characterize effects as one or the other, and how the system itself is
defined may further confuse the distinction. However, by defining correlated feed-
back as a key property of a CAS, we bypass this argument in favor of defining what
the feedback represents, and what it tells us about the system.
If an external effect sets off a chain reaction of persistent patterns, then the un-
derlying properties that allow this chain reaction to occur are of distinct interest for
understanding the system. If, however, there is persistent and recognizable feedback
that comes from outside of the system, then we consider this feedback to be sig-
nificant regarding our understanding of the system properties. Therefore, when we
define a system, we use the method and type of feedback as a key attribute.
Consider the example of a marketplace. Such a system may encompass agents
that buy and sell products, or stock in companies; it may include the concept of
wealth, earnings, inflation, etc.; and it may also be affected by regulatory bodies,
such as the Federal Reserve. If one defines the system as only the agents and how
they interact with each other, then the actions of a Federal Reserve would be exoge-
nous to this system. However, these actions by the Federal Reserve whatever they
may be are clearly influenced by the state of the market. Furthermore, they are
likewise designed to influence the future state of that market. This is a significant
level of feedback that should be accounted for when studying the system, i.e., the
12 Ted Carmichael and Mirsad Hadˇ
Another way of determining whether certain factors are exogenous or endoge-
nous to the system is to consider whether or not the feedback goes both ways: the
agents affect the environment even while the environment affects the agents. This is
distinct from a model of, say, an ecology which has sunlight as an external factor.
The sun cycles through day and night, as well as annual cycles of summer and win-
ter, and these cycles generally affect the behavior of most ecological systems. But
the agents in this system cannot truly affect the behavior of the sun. While defining
what encompasses a system, and what potential factors are internal or external to
that system, it is more important to note the level of feedback that exists between
those factors, as this is both definitional and functional to the system being studied.
2.7 Emergence and Self-Organization
The term emergence, like complexity, has not yet reached a consensus definition.
Some researchers distinguish between weak emergence and strong emergence, and
use this definition as representing a fundamental law.
If there are phenomena that are strongly emergent [emphasis added] with respect to the
domain of physics, then our conception of nature needs to be expanded to accommodate
them. That is, if there are phenomena whose existence is not deducible from the facts about
the exact distribution of particles and fields throughout space and [time] (along with the laws
of physics), then this suggests that new fundamental laws of nature are needed to explain
these phenomena [6, p. 1].
This idea would seem to indicate that a strongly emergent property is similar to
the idea of gravity: gravity is a fundamental law, a property of matter; but gravity
is only apparent as one particle relates to another. In this view, it is not that the rule
cannot be modeled by the agent, but rather it cannot be understood except in terms
of other agents.
In our definition of emergent behavior, we adopt this idea of relations among
agents in the system, as in the way we have previously defined correlated interac-
tions. A traffic pattern cannot really exist with only one car, and a colony of ants
cannot be said to find food if there is only one ant. In this way, emergent behavior
is a property of a system that is at a different scale than the parts of the system [19].
In a similar vein, emergence is the macro-level behavior that is not defined at the
macro-level, but rather depends upon the rules and interactions of agents defined at
the micro-level.
Consider a few examples of typical emergent behavior. There are the cars as
agents, in the example cited previously. There is also the example of bees or ants,
following simple rules to forge for food or build a nest. Johnson talks at length about
the city of Manchester, England, during the 19th century [15]. He uses it to illustrate
how a city with tens of thousands of people, yet absolutely no central planning, still
managed to organize itself in distinct patterns, such as areas of the working class
separate from the nicer middle-class neighborhoods.
The Fundamentals of Complex Adaptive Systems 13
The city is complex because it has a coherent personality, a personality that self-organizes
out of millions of individual decisions, a global order built out of local interactions [15, p.
The brain is also often cited as a complex, adaptive system, with intelligence (or
even some sub-set of intelligence, such as vision) as an emergent feature. In our CAS
models, we look at a number of emergent features, such as the self-organization of
the agents and the aggregate behavior of the system [5, 3, 4].
The self in self-organization refers to the state of an individual agent in a com-
plex system. This agent follows its own local rules, and uses its own own attributes
in applying those rules. Let us consider a simple model of an ant colony. For the
purposes of illustration, this model need not be realistic. Assume each individual
ant has the same three rules: 1) search randomly across the environment for food;
2) if you find food, carry it back to the colony and leave a scent trail; 3) if you find
a scent trail, follow it until you find food.
If one ant finds food, then this new attribute “I have food” activates the
rule to carry a piece of the food back to the colony and leave a scent trail. Now,
by leaving the scent trail, this ant can affect the current state of any other ant that
happens upon that trail. A new ant, finding the scent trail, will activate its own rule
to follow that trail to the food source, at which point it will also carry a piece back
to the colony, and add to the trail. In this way, a significant subset of the ant colony
organizes itself to systematically collect the food and bring it back to the colony.
The individual agents in this case, the ants are acting with limited knowledge
and simple rules. But by providing feedback to other agents, and influencing them
to act in similar ways, they produce the correlations of behavior that represent the
organization of the overall system; i.e., the self-organization that emerges from these
interactions, defining the local increase in complexity.
2.8 Natural Biases of Complex Systems
The framework of CAS directly challenges two distinct biases that tend to affect
our understanding of the agents in a complex system: 1) a hierarchical bias; and 2)
a complexity bias. A hierarchical bias can be illustrated by the tendency to view a
complex system in terms of a leader directing the activities of all the other agents.
As Johnson points out, colonies of ants have previously been viewed as the queen
controlling the colony as a whole; however, this fails to capture the amount of au-
tonomy present among the other ants [15]. And, with a little reflection, it becomes
obvious that a queen ant simply would not have the bandwidth necessary to com-
municate to all the other ants, and direct them in their daily tasks. Fundamentals
of information theory demonstrate that such would be impossible. Most ants do not
come into contact with the queen, and they do not have much to say when they do.
Only a few things can be communicated via pheromones that ants exchange, and
complicated task lists are not among them.
14 Ted Carmichael and Mirsad Hadˇ
In much the same way, the growth of Manchester previously mentioned, and the
distinctions that emerged between, say, rich and poor neighborhoods, was deeply
surprising to those who thought that such patterns of growth could only be achieved
by directed action, through some sort of governing body.
These strange phenomena global properties of systems as represented in the
growth of Manchester, or Smiths invisible hand theory did not go unnoticed or
unstudied. However, as with the peculiar behavior of the slime mold, researchers
struggled to frame a model that could explain these global effects using a hierar-
chy that they intuitively felt must exist. The development of CAS tools and models,
therefore, represent a new methodology to remedy the shortcomings of previous
methods. We no longer have to assume that the behavior is directed in a hierarchi-
cal fashion. Distributed intelligence and decision-making does not require a central
governing authority. Correlated feedbacks among autonomous agents are enough to
describe and model these behaviors.
CAS methods of analysis also help resist the complexity bias for hypothesized
agents that is often found when studying complex systems. This is closely related
to the hierarchical bias, in that leader-agents are assumed to be more complex, to
account for the level of control needed in a leadership model. In other words, the
leader must be smarter: more capable and more complicated. Also, the required
network among such agents would be, by necessity, more complicated and long-
reaching, to allow for instructions to be passed to each agent in the system. If one is
to assume a hierarchical system in, say, an ant colony, then the modeler must answer
the question: how are orders conveyed to each worker ant? The consequences of a
complexity bias is a more unwieldy, computationally expensive, and fragile model.
A CAS is inherently simpler. Each ant does not need instructions; rather, they
can be programmed with just a few rules of behavior. In such a model, the ants do
not even have to be aware of the state of the colony as a whole; they only need to
know their own current state and apply that information to their current environment.
Similarly, a slime-mode model doesnt require a complex pacemaker cell if a simpler
CAS model is able to replicate the organisms complex behavior without it.
This release from both the hierarchical bias and complexity bias in the agent-
level description of a system is more satisfying, as it follows Occams Razor: the
simplest explanation for a phenomenon is the preferred one. And the beauty of this
paradigm is also found in the fact that the simpler explanation the emergent, dis-
tributed explanation is also less expensive to implement. Fitness functions that
are inherent in nature are always pushing the system, any system, toward more effi-
cient use of resources. And thousands of autonomous, simple ants that dont require
constant instruction are surely more efficient and more robust than a model
that has one central, complicated, irreplaceable, and over-worked queen.
The Fundamentals of Complex Adaptive Systems 15
3 Conclusions
The assumptions inherent in Complex Adaptive Systems have allowed us to more
productively study challenging and complex phenomena, in both nature and so-
ciety. It has allowed us to uncover intriguing similarities across domains that are
seemingly far apart. And it allows us to focus on the agent primitives in our models,
as direct analogues to real-world behavior. This inherent transparency is a key fea-
ture of Agent-based Modeling, as an antidote to black box simulations that may be
correct, but are by definition obscure and hard to analyze.
By using the CAS paradigm, with correlated feedbacks among simpler agents,
then the features of the system of interest are allowed to emerge from dynamic
agent interactions, as they do in the real world, rather than be dictated in a top-
down, complicated manner. Ultimately, this gives our models the inherent flexibility
needed to simulate systems even when conditions are different than expected. This
flexibility makes our models more fundamentally robust, able to adapt to a variety
of environments, only some of which may be anticipated. Thus, the CAS approach,
and its inherent flexibility and distributed robustness, creates models that can capture
results we did not already expect to see.
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... For resilience see Bartuseviciene et al. (2022), Comfort et al. (2010), Hohenstein et al. (2015), and Powley et al. (2020). 3 For concepts and cases of complex adaptive systems see Carmichael and Hadzikadic (2019) and McMillan (2004), Cunha and Cunha (2006) and Comfort (2019). 4 Some of these descriptions are Consolini (1991), LaPorte (1996), Schulman (1993), Roe andSchulman (2008, 2016), Hopkins (2009) and MacRae (2014). ...
... In this and more recent formulations of forward adaptation, resilience is often described as founded on collective action occurring in different frames than that of single organizations, often in surrounding socio-technical systems. In fact, some resilience theorists now define "complex adaptive systems" as those with resilience as their primary ongoing feature in the face of rapidly changing, turbulent and uncertain environments (Comfort et al., 2010;Carmichael and Hadzikadic, 2019;Ansell et al., 2017). In assessing resilience in the context of multiorganizational networks it is important to contrast these networks with evolving models of complex adaptive systems. ...
... Finally, emergence in most MAS models is usually mentioned only as something to be avoided, if possible, rather than as an inherent, key property of the system. In CAS, emergence is considered a feature, not a bug." (Carmichael and Hadzikadic, 2019). ...
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Both reliability and resilience have become popular concepts in the study of organizations. They have also been applied as performance standards to the assessment of particular organizations, often retrospectively in relation to their role in crisis situations or major disruptive events. Yet this essay argues that the concepts, reliability and resilience, as generally understood and applied to single organizations, have uncertain application to the ever-growing number of organizational networks. In this essay we will look particularly at: networks of contracted services or technology from private-sector organizations by government agencies or by other private organizations , interconnected critical infrastructure organizations, long-linked production and supply chains of various products and services, and interacting governments and private organizations in emergency management after natural disasters. The analysis of these networks will center around answering two basic and contrasting questions: A. Will the capacities for reliability or resilience of individual organizations within an organizational network create that capacity for the network overall to be reliable and resilient, and therefore, is improving individual organizational reliability and resilience an effective strategy for creating a more reliable and resilient organizational network as a whole? Or: B. Is it instead a paradox of organizational networks that unless reliability and resilience are first achieved as network properties, it is unlikely that the individual organizations in a network can themselves become reliable and resilient? The essay explores both questions in relation to current concepts of reliability (high-lighting high reliability organizations research) and resilience (of various types, including concepts of complex adaptive systems) and with illustrations from supply chains, interconnected infrastructures, contracted services, and emergency management networks. The essay concludes with an argument that current concepts of both reliability and resilience are ambiguous and incompletely specified-not clearly and fully enough developed to allow confident answers either question A or B. This, in itself, is a condition with both conceptual and practical implications, one that should compel further conceptual and case research.
... Given the continued pressure on healthcare systems worldwide and the potential impact of effective QI, it seems important to explore all options thoroughly. Carmichael and Hadžikadić (2019) suggest that systems thinking is vulnerable to hierarchical and complexity biases, that is, we tend to introduce hierarchy and complexity into our systems thinking whether or not this is justified. In contrast, explanations of natural CAS behavior are usually associated with a small set of agent rules and avoid hierarchical agent structure (Holland 2006). ...
... Context and enabling factors leadership hierarchy through the filters of our sociotechnical norms such as leadership and decision-making. Directly harnessing CAS phenomena, free from hierarchical and complexity biases, is a valid and still under-explored alternative strategy (Carmichael and Hadžikadić 2019). Skepticism toward the applicability of CAS principles within human sociotechnical contexts is rare in the literature but does exist and raises valid concerns. ...
... Therefore, the ability of the simulated agent network to successfully reach the improvement target directly supports H1. System learning was managed at the agent behavior level of granularity, without recourse to agent hierarchy or more complex agent rules (Carmichael and Hadžikadić 2019). ...
The healthcare quality improvement (QI) literature is replete with examples stating that continued failure to regard healthcare as a complex adaptive system (CAS) reduces the effectiveness of quality improvement initiatives. Recommendations and strategies for managing change within CAS exist but the specific mechanisms that bring about successful change within CAS and the implications for quality practitioners are under-explored. This article presents a generalizable model for QI within CAS and provides a specifically CAS explanation for incremental change. We develop a conceptual model from foundational CAS principles that is then operationalized as an agent-based simulation model. Our model captures critical complex system behavior in a generic manner easily applied to different improvement contexts. We tested that model using a recognizably complex healthcare improvement case: reducing antipsychotic prescribing levels in aged residential care. Non-linear phase transitions were observed, conditioned on the network’s ability to learn solution options and simultaneously maintain cooperation. We believe that the conceptual framework of our model can assist practitioners navigating complex QI activities.
... Complex adaptive processes are influenced by endogenous and/or exogenous interactions (Carmichael and Hadžikadić, 2019), and in the literature, a variety of theoretical models have been used as a foundation to explore such interactions. As noted in sections 2 and 3 of this paper, it is recognized that some of these models only offer a partial view, and in the following discussion the SDL-based service systems model shown in figure 1 will be used as a holistic framework to suggest connections between these partial views. ...
This paper considers one aspect of UN SustainableDevelopment Goal SDG7 - the intention to \textquotesingle leave no-onebehind\textquotesingle{} in the transition to renewable energy. Thetarget beneficiaries have access to affordable electricity restricted insome way. Two examples of affordable innovation based on artificialintelligence-driven microgrid technology serving clients in developingand developed economies are presented. These initiatives provide directeconomic, environmental and social benefits, but also add to the quantumof renewable energy generated in their local areas. A multiplicity ofcommunity, enterprise and government actors cooperate in establishingand operating the particular programs described, and community benefitsextend beyond simple economic outcomes, e.g., building social capitaland trust in the technology. A model characterizing a broader view ofSDG 7 realization dynamics is presented. This includes theidentification of four kinds of learning space and the notion of tippingpoints, which may be topics for further research.
... Next to these referenced classic approaches, the complexity of the innovation ecosystem concept is also indicated by several of latest research, pointing out the complex feature of the different actors, the multi-variable nature of their cooperation, the specific activities and value creation characteristics of the ecosystem, whilst the role of co-development and co-evolution, the innovation-driven focus on results (output products and services), and the duality of competition and R&D are still relevant aspects. See works of Jucevicius and Grumadaite [6], Bonnici [7], Carmichael and Hadzikadic [8] in this topic. ...
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... The complexity of systems arises from the inherent challenge of accurately analyzing their internal connections, making them difficult to model [2,3]. In a complex system, every component plays a crucial role in the overall functioning, yet each individual component can be understood independently of others [4]. In the field of network research, networks that exhibit a large number of interconnected nodes and intricate relationships between them are referred to as complex networks [5,6]. ...
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... Complex Adaptive Systems (CAS) is a framework for understanding systems of agents that collectively combine to form emergent, global level properties (Carmichael & Hadzikadic, 2019). Food system is one of the complex systems that necessitates a theoretic viewpoint to focus on. ...
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The food system is one of the complex systems that require a theoretic perspective. The core objective of the study was to identify an emergent feature described by the variables: total foodborne diseases, and health care expenditure in the 16 regions of the Philippines. This study employed the descriptive-analytic research, utilized data mining, factor analysis, cluster analysis, and complex adaptive systems. Factor analysis results revealed that the factor or feature outlines a foodborne disease allocation. Two clusters were generated using cluster analysis. The first cluster comprised regions with foodborne diseases ranging from 212-890 incidences, and the second cluster contained regions with 1338 to 4770 foodborne disease cases. National Capital Region (NCR), MIMAROPA, Regions 1, 2, 3, 5, 8, and 11 belonged to the cluster with lower incidences of foodborne diseases. These regions also had high positive synergy. Results also revealed that Regions 4, 6, 7, 9, 10, 12, CAR, and CARAGA had higher foodborne disease cases which correspondingly showed extensive distinctions among regions. The emerging pattern appeared to be random albeit cyclical in nature with no upward nor downward drift. This demonstrated an amplitude and slight upward drift as well. To sum, it was detected that there are two emergent patterns in budgetary allocation for foodborne diseases in the Philippines: those regions for which budgetary allocation for foodborne diseases were not based on actual incidences of the diseases, and those regions for which budgetary allocation were more sensitive to the incidence of foodborne diseases.
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Background Despite three decades of policy initiatives to improve integration of health care, delivery of health care in New Zealand remains fragmented, and health inequities persist for Māori and other high priority populations. An evidence base is needed to increase the chances of success with implementation of large-system transformation (LST) initiatives in a complex adaptive system. Methods This research aimed to identify key elements that support implementation of LST initiatives, and to investigate contextual factors that influence these initiatives. The realist logic of enquiry, nested within the macro framing of complex adaptive systems, formed the overall methodology for this research and involved five phases: theory gleaning from a local LST initiative, literature review, interviews, workshop, and online survey. We explained variations in success (outcomes) by identifying mechanisms triggered by various contexts in which LST initiatives are implemented. Results The research found that a set of 10 key elements needs to be present in the New Zealand health system to increase chances of success with implementation of LST initiatives. These are: (i) an alliancing way of working; (ii) a commitment to te Tiriti o Waitangi; (iii) an understanding of equity; (iv) clinical leadership and involvement; (v) involved people, whānau, and community; (vi) intelligent commissioning; (vii) continuous improvement; (viii) integrated health information; (ix) analytic capability; and (x) dedicated resources and time. The research identified five contextual factors that influenced implementation of LST initiatives: a history of working together, distributed leadership from funders, the maturity of Alliances, capacity and capability for improvement, and a continuous improvement culture. Conclusions Use of informal trust-based networks provided a critical platform for successful implementation of LST initiatives in the New Zealand health system. Maturity of these networks depends on the key mechanism of trust, that is built and nurtured over time through sharing of power by senior health leaders by practising distributed leadership. The role of central agencies and government is to provide the policy settings and conditions in which trust-based networks can flourish. The evidence base for successful implementation of LST initiatives produced in this research is transferrable to other regions and countries.
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The demands of many public health contexts and challenges call for conditions that foster effective decision making. Policy designers must make appropriate choices appear viable, accessible, and beneficial. They can do this by harnessing transdisciplinary knowledge about behavioral tendencies, simultaneously integrating insights into end users and non-human agents, and employing design methods for system-level solutions. We propose a "choice triad" model to help practitioners frame transdisciplinary approaches to complex public health challenges and design effective conditions for choice. It has three lenses: choice posture, to reveal human and non-human agents' predispositions and inclinations; choice architecture, to improve immediate choice environments and encourage preferred actions; and choice infrastructure, to reveal the underlying system structures, processes, and policies that shape how potential public health solutions are accessed and supported. This approach promises to augment traditional design tools and expand current conceptions of available "economies of choice" when crafting behavioral public policy solutions. In combination, these lenses can provide a new conceptual syntax and working model to diagnose and develop solutions within complex public health settings. We introduce two examples to illustrate this model: the water crisis in Flint, Michigan, and Covid-19 vaccination efforts in the United States. Keywords: Design for policy, Systemic policy design, Behavioral design, Choice infrastructure, Choice triad model, Public health policy
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Computer simulations of complex food-webs are an important tool for deepening our understanding of these systems. Yet most computer models assume, rather than generate, key system-level patterns, or use mathematical modeling approaches that make it difficult to account for non-linearities. In this article we present a computer simulation model that addresses these concerns by using Agent-Based Modeling techniques, so that system-level patterns emerge from the interactions of thousands of individual simulated agents. In previous work this model replicated fundamental properties of an ecosystem. This work extends the model in the context of the Red Queen Hypothesis. We find that improvements in the competitive landscape for a single predator agent does not generally confer a benefit on the species as a whole, and may even be detrimental. Additional experiments that explicitly account for energy requirements and allow individual evolution illustrate how the arms race may be limited by natural means. This model can serve as a platform for evaluating policy options for developing sustainable systems, both in terms of long-term and short-term desired outcomes.
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It is sometimes difficult to convey to those outside of complexity studies what exactly is meant by emergence, agents, bottom-up processes, or even the phrase agent-based models itself. Part of this is due to these terms (and others) being overused. They have differing definitions across disciplines - sometimes overlapping, sometimes not - reflecting different scopes, purposes, and perspectives prevalent in these fields of study. Sometimes these terms are only vaguely defined. At other times they are defined precisely, but too narrowly to be very useful in other fields.
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The economic impact of traffic management grows each day. Infrastructure improvements are costly, hence any such project must be carefully evaluated for its impact on the traffic. Emphasis on traffic simulation tools has increased in the last five years to help evaluate new traffic-control strategies, as well as planned road constructions. Building high-quality traffic simulations has several challenges, including computational performance, the accuracy of models in representing the traffic flow, and the difficulty of integration with advanced traffic management and traffic information systems. In this paper, we report on our work on an agent-based approach to traffic simulation, and how it addresses these issues.
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Computer simulations of complex food-webs are important tools for deepening our understanding of these systems. Yet most computer models assume, rather than generate, key system-level patterns, or use mathematical modeling approaches that make it difficult to account fully for non-linear dynamics. In this article we present a computer simulation model that addresses these concerns by focusing on assumptions of agent attributes rather than agent outcomes. Our model utilizes the techniques of Complex Adaptive Systems and Agent-Based Modeling so that system level patterns of a marine ecosystem emerge from the interactions of thousands of individual computer agents. This methodology is validated by using this general simulation model to replicate fundamental properties of a marine ecosystem, including: (1) the predator-prey oscillations found in Lotka-Volterra; (2) the stepped pattern of biomass accrual from resource enrichment; (3) the Paradox of Enrichment; and (4) Gause's Law.
It is suggested that a system of chemical substances, called morphogens, reacting together and diffusing through a tissue, is adequate to account for the main phenomena of morphogenesis. Such a system, although it may originally be quite homogeneous, may later develop a pattern or structure due to an instability of the homogeneous equilibrium, which is triggered off by random disturbances. Such reaction-diffusion systems are considered in some detail in the case of an isolated ring of cells, a mathematically convenient, though biologically unusual system. The investigation is chiefly concerned with the onset of instability. It is found that there are six essentially different forms which this may take. In the most interesting form stationary waves appear on the ring. It is suggested that this might account, for instance, for the tentacle patterns on Hydra and for whorled leaves. A system of reactions and diffusion on a sphere is also considered. Such a system appears to account for gastrulation. Another reaction system in two dimensions gives rise to patterns reminiscent of dappling. It is also suggested that stationary waves in two dimensions could account for the phenomena of phyllotaxis. The purpose of this paper is to discuss a possible mechanism by which the genes of a zygote may determine the anatomical structure of the resulting organism. The theory does not make any new hypotheses; it merely suggests that certain well-known physical laws are sufficient to account for many of the facts. The full understanding of the paper requires a good knowledge of mathematics, some biology, and some elementary chemistry. Since readers cannot be expected to be experts in all of these subjects, a number of elementary facts are explained, which can be found in text-books, but whose omission would make the paper difficult reading.
Agent-based computational modeling is changing the face of social science. In Generative Social Science, Joshua Epstein argues that this powerful, novel technique permits the social sciences to meet a fundamentally new standard of explanation, in which one "grows" the phenomenon of interest in an artificial society of interacting agents: heterogeneous, boundedly rational actors, represented as mathematical or software objects. After elaborating this notion of generative explanation in a pair of overarching foundational chapters, Epstein illustrates it with examples chosen from such far-flung fields as archaeology, civil conflict, the evolution of norms, epidemiology, retirement economics, spatial games, and organizational adaptation. In elegant chapter preludes, he explains how these widely diverse modeling studies support his sweeping case for generative explanation. This book represents a powerful consolidation of Epstein's interdisciplinary research activities in the decade since the publication of his and Robert Axtell's landmark volume, Growing Artificial Societies. Beautifully illustrated, Generative Social Science includes a CD that contains animated movies of core model runs, and programs allowing users to easily change assumptions and explore models, making it an invaluable text for courses in modeling at all levels.
Some segregation results from the practices of organizations, some from specialized communication systems, some from correlation with a variable that is non‐random; and some results from the interplay of individual choices. This is an abstract study of the interactive dynamics of discriminatory individual choices. One model is a simulation in which individual members of two recognizable groups distribute themselves in neighborhoods defined by reference to their own locations. A second model is analytic and deals with compartmented space. A final section applies the analytics to ‘neighborhood tipping.’ The systemic effects are found to be overwhelming: there is no simple correspondence of individual incentive to collective results. Exaggerated separation and patterning result from the dynamics of movement. Inferences about individual motives can usually not be drawn from aggregate patterns. Some unexpected phenomena, like density and vacancy, are generated. A general theory of ‘tipping’ begins to emerge.