Complex Systems
"We're not looking for the meaning of life, more the meaning in life, the generation of order, the generation of pattern, the quality of the organism. The fundamental problem of biology is how you generate form."
-- Brian Goodwin

Good News !!

You are viewing a draft of the book entitled "Patterns – The Art, Soul, and Science of Beholding Nature". The final version of this book has now being published as an Amazon Kindle eBook.

There are some significant changes in the eBook that are not in this draft. You may purchase the eBook here

Some of the ideas in the eBook are contained in posts at my Patterns In Nature Blog. You are encouraged to visit this blog site. If you press the "Like" button shown below, your Facebook page will provide you with short notifications and summaries of new blog posts as they become available.

Patterns in nature are described as "complex systems" because they are composed of complicated and connected structures with highly ordered dynamic properties. In many cases, this complexity results in an emergent behavior or structure that manifests a mega-form or superorganism of some sort. Ecosystems at all levels are good examples of patterns in nature that are complex systems. This Romanseco Brocolli is a familiar example of a highly complex structure that exhibits order both in its spiral layout and in its self similar fractal nature.

Complexity is the study of how relatively simple behavior is generated from extremely complicated, apparently chaotic systems. The goal of complexity science is to define patterns in the networks of connectivity that are contained within complex systems.The study of complex systems cuts across all traditional disciplines of science. It focuses on certain questions about parts, wholes and relationships. Complexity studies focus on the simplicity in the dynamic process of pattern formation instead of the pattern's static structure. The relationships between components in a complex system are generally more important than the components themselves because local rules regarding connectivity generate global order.

In Amaral's excellent review paper on complex networks, simple, complicated and complex systems are described and compared. Simple systems have a small number of components that act according to well understood laws. A pendulum is a simple system because it has one part and operates according to Newton's equations of motion. Complicated systems are defined as "having a large number of components which have well defined roles and are governed by well-understood rules". All parts work in unison to achieve a goal, have a limited range of response to environmental changes, and require a leader. The Boeing 747 is an example of a complicated system with over 3 million parts where the crew is the leader and is the external force that effects adjustments under extraordinary circumstances.

In contrast to a complicated system, a complex system "is a system with a large number of elements...capable of interacting with each other and adapting to their environment without a leader or a blueprint. The interaction between elements may occur only with immediate neighbors or distant ones; the agents can be all identical or different; they may move in space or occupy fixed positions, and can be in one of two states or have multiple states. The common characteristic of all complex systems is that they display organization without any external organizing principle being applied. The whole is much more than the sum of its parts.... Migrating geese self-organize without the need for a leader to tell the rest of the flock what to do. Roles in the flock are fluid and one goose at the head of the formation will quickly be replaced by the flock a great deal of robustness as no single goose is essential for the flock's success during the migration."

A complex system exhibits one or more properties that are not obvious from an examination of the behaviors of the individual parts. No amount of information at the level of the individual component can reveal the organizational pattern of the system. Yet, paradoxically, it is the combined behaviors and interactions of individual components that define behaviors at a system level. The resulting behaviors of the system are called emergent behavior.

The key to the successful operation of a complex system is the connectivity between its components. Consequently, the use of network theory has become an important part of the study of complex systems. A ubiquitous characteristic of networks in complex systems is the "small-world" phenomena -- a mixture of two apparently incompatible network architectures. Here, a highly ordered network structure is mixed with a random network. First, there is large local clustering of elements where there is an overlap of groups of neighbors. This arrangement is typical of highly ordered lattice network arrangements. Second, the number of intermediate links between any pair of elements is quite small. This second characteristic is typical of random graphs.

All complex systems share the following features:

  • The components of complex systems are bound together by similar network architectures.
  • Boundaries are difficult to determine.
  • Usually are open systems that interact with their environment.
  • Are dynamic -- they change over time.
  • They act like feedback machines -- prior states have an influence on present states.
  • Exhibit emergent phenomena.
  • Computer simulation is the tool typically used to study complex systems.
  • The system may contain chaotic components.

While the study of complexity is the study of how complicated natural patterns result from simple behaviors of connected individuals within a system, chaos is the study of how simple patterns can generate complicated behavior. Chaos theory is involves finding the underlying order in apparently random data. Chaos is a very important concept because it helps us to understand and simplify complex patterns in nature.

The two videos below describe the reasons why the study of complex systems is so important

Useful References


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