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.
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2 Ted Carmichael and Mirsad Hadˇ
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
•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 , 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  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 , 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 , which they expanded upon
in . 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.
 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 
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 . 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 . 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 . 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 .
This endeavor is similar in scope to the work of Nicolis and Prigongine .
As described by , 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  is most similar to that used previously by
Axelrod et al. . 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
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-
The primary difﬁculty with  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
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 . 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 .
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 . 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.
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
The most general distinction we use refers to Warren Weavers division of com-
plexity into two types: disorganized complexity and organized complexity . 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.
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 . 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) .
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
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  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.
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 .
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
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 . 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 . 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
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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