Diagram: Iterations


CAS systems unfold over time, with agents continuously adjusting behaviors in response to feedback. Each iteration moves the system towards more coordinate, complex behaviors.

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One of the keys to complex adaptation occurring is the ability for the system to manifest emergent behaviors as a result of feedback.

There are a series of ways in which we can think about this feedback, each of which tie in with the concept of iterations. In all cases, we see emergent phenomena arising over the course of multiple iterations. However, each case differs in terms of how tightly coupled the emergent phenomena is with the notion of 'learning'. Thus, we can understand emergent global features as a result of the following kinds of dynamics:

- produced solely due to the interaction of a rule system acting upon itself over multiple iterations - without regard to 'learning' or 'fitness' (example: Fractals,{{game-of-life}} HANDLEBAR FAIL );

- produced solely by virtue of natural, physical laws that, when enacted in a system composed of multiple agents sharing a common context AND with other agent behavior forming a feature of this context. Agents, over iterative adjustments, gradually coallesce towards regimes that minimize unnecessary energy expenditure in the system (example: metronomes on sliding platform going into sync, {{benard-rolls}} HANDLEBAR FAIL forming in heated liquid).

- produced solely by virtue of static rule regimes that steer agent behavior in a system composed of multiple agents sharing a common context AND with other agent behavior forming a feature of this context). Agents, over iterative adjustments,  gradually coallesce towards regimes that,  while not necessarily the most efficient, are the best available to the system based on the global knowledge available (example: ants forming ant trails, flocking behaviors).

Finally, we have the last concept, where emergent global features are most closely produced by learning, such that:

- by iteratively applying rule regimes and then evaluating the effectiveness of these regimes in light of feedback, agents evolve their rule regimes to better align their response to inputs with outputs regime that effectively achieve a particular goal with maximum effectiveness for minimum costs (Darwinian evolution, Firm Competition).

Let us look at the first case, a rule system acting upon itself over multiple iterations. These kinds of examples are often found in artificially generated systems that exhibit complex features. Take for example the koch curve:

First four iterations of the Koch Curve

We begin with a line and a simple three step rule protocol:

- for every line segment break it into three equal segments;

- Form an equilateral triangle wherever the center segment falls (removing the base)
- Repeat this process for each of the newly created line segments.

As seen in the image above, over multiple iterations a high degree of complexity is generated. The same principles are at work in creating all fractal forms - basic instructions generate an output, whose new properties (going from one line segment to four line segments), become the new context upon which to re-apply the rule.

While we do get a lot of richness from such phenomena, it would be incorrect to state that the resulting figure 'adapts' or 'learns' - it simply 'unfolds' over multiple iterations.

Similarly, we can create a very simple agent-based model, a grid composed of cells that follow basic rules that turn a given cell on the grid either 'on' or 'off' and let it unfold step by step. As long as the behavior at each time step is predicated on the outcome generated at the previous time step, we are able to create incredibly interesting phenomena. Conway's Game of Life (see {{rules/schemata}} is a prime example of complexity generated by such simple rules, that, when repeated over multiple time steps yields highly complex behaviors.

This famous example of emergent complexity is entitle 'the game of life', but is it really life? While the emergent outcomes of the automata are rich in variety, can we say that the system truly adapts or learns? One feature of the output is that some patterns create iterative loops, which reproduce the identical patterns - meaning that once these forms emerge they can reproduce themselves. If proliferation within the grid of the game is considered to be a form of higher evolution, then this might be seen as a form of adaptation.

Game of Life from Wikimedia Commons

Other kinds of complex systems are formed of co-mingled agents that are simply behaving in accordance with the energetic forces they are interacting with. Thus certain chemical reactions will...

to We also see see systems that are composed of static rules, but where these rules

What is truly interesting in complex adaptive systems is the way in which a rules can adjust over multiple generations. In order for this to occur, agents within the system need to have a kind of goal - an outcome that is preferred over others. In the example of the koch curve above, we cannot say that the line segments have a 'goal' of creating a particular kind of shape that is preferred over any other. The system has an emergent quality, but this emergent is in no way purposeful in and of itself.

But in CAS, the agents do have desired outcomes or more 'fit' states. Fitness is a useful concept here, because 'goal' implies volition on the part of the agents. This is fine for some kinds of agents - an ant has the goal of finding food - but not all. Water molecules don't have goals, but they can enter into more 'fit' behavioral states in the context with their environment.

Iterative complex systems, where agents shift their according to

We  . We can think of these goals as The word 'goal' can be problematic since Each time a rule is enacted within a given context, the results of that enactment change the context. In a complex adaptive system the comparison of the new context with the rule


Photo Credit and Caption: Underwater image of fish in Moofushi Kandu, Maldives, by Bruno de Giusti (via Wikimedia Commons)

Cite this page:

Wohl, S. (2019, 13 November). Iterations. Retrieved from https://kapalicarsi.wittmeyer.io/definition/timeiterations

Iterations was updated November 13th, 2019.

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