"The pattern which connects is a meta-pattern. It is a pattern of patterns. It is that meta-pattern which defines the vast generalization that, indeed, it is patterns which connect"
-- Gregory Bateson, "Mind and Nature"
Networks are the underlying structure of complex systems that we commonly refer to as patterns in nature. These complex networks are composed of both a physical architecture (form) and the associated dynamic processes (function) that control and connect the pattern components within the system. Understanding these patterns comes from looking at both the structural and the dynamic relationships within these networks. This web page discusses the dynamics of networks within nature's patterns. The page on network architecture explores the structure of these networks.
Nature's networks are not static or in equilibrium. Instead, they are dynamic entities which are constantly growing, directing the flow of processes and energy, and sometimes altering their wiring. These complex dynamic systems are ubiquitous in nature. In social networks, people are born, die, and move to new locations. The Internet acquires new nodes and hyperlinks over time. Protein interactions are subject to evolution. Epidemics change their course and the rate of infection. River systems are flowing networks of water that are affected by erosion and other dynamic processes that occur over time.
In these and other networks, the states of both the network nodes and their links can change with time. And, the topology of the network often evolves with time. These changes are typically governed by local rules that are both non-linear and heterogeneous across the network. The result is the emergence of a highly complex, dynamic, and adaptive system whose global properties are not pre-specified by network design and are difficult or impossible to predict from knowledge of the individual parts or subsystems.
A vivid demonstration of the dynamics of a network is a school of fish. Here, the fish are modeled as nodes in the network. The self organizing energy between fish comes from its eyes which provide visual cues and its lateral line which senses proximity to another body. The network links model that energy. Following a set of rules, the eyes and the lateral line sense proximity to its neighbors (and to a predator) and cause the fish to make corrections to its swimming energies. This local energy results in a simultaneity of events or motions in the school which we know as synchrony.
A complex system’s global behavior arises from the collective actions of simple components, and to the mapping from individual actions to collective behavior by way of the network. Large numbers of agents interacting locally give rise to network structures, self organizing in such a way so as to bring forth larger dynamically coherent globally emergent patterns. Large changes in dynamic behavior at a system level can be caused by small modifications in local dynamics. These modifications may not be perceptible to the individual agents within the system that have only local knowledge of the network. An excellent example is the effect of a predator on a fish school where only a few fish are aware of the predator. Yet, the form and speed of the entire school changes to avoid the predator.
In her paper "Complex Systems: Network Thinking", Melanie Mitchell provides an excellent example of a complex dynamic network as she provides a description (paraphrased here) of the foraging dynamics within an ant colony. These dynamics are indeed patterns in nature.
"An ant colony can be considered as a network of relatively simple elements (ants) from which emerge larger-scale intelligent and adaptive behaviors. An example of such behavior in ant colonies is the ability to optimally and adaptively allocate resources (ants) in foraging for food... a behavior accomplished with no central control....
Foraging ants in a colony set out moving randomly in different directions. When an ant encounters a food source, it returns to the nest, leaving a pheromone trail. When other ants encounter a pheromone trail, they are likely to follow it. The greater the concentration of pheromone, the more likely an ant will be to follow the trail. If an ant encounters the food source, it returns to the nest, reinforcing the trail. In the absence of reinforcement, a pheromone trail will dissipate. In this way, ants collectively build up and communicate information about the locations and quality of different food sources, and this information adapts to changes in these environmental conditions. At any given time, the existing trails and their strengths form a good model of the food environment discovered collectively by the foragers."
Task allocation is another way in which an ant colony regulates its own behavior in a decentralized way. Red Harvester ant workers in these colonies divide themselves among four types of tasks: foraging, nest maintenance, patrolling, and midden (refuse sorting) work. The numbers of workers pursuing each type of task adapts to changes in the environment. If the nest is disturbed in some small way, the number of nest maintenance workers will increase. Likewise, if the food supply in the neighborhood is large and high quality, the number of foragers will increase.
Much research has been done on the architecture of low dimensional networks such as lattices and random graphs. However, relatively little investigation has taken place in the field of large complex dynamic networks. Much of this new research is on a theoretical and conceptual level. Below is a summary of findings in recent network studies
- There is a new focus on the properties or real-world networks asking empirical as well as theoretical questions.
- Networks are not static, but evolve with time according to various dynamic rules.
- Networks are the framework upon which real-world distributed dynamical systems are built.
- Networks arise naturally, evolving in a manner that is unplanned and decentralized.
- Many networks are the product of dynamical processes that add or remove vertices or edges.
- Processes that operate at a local level both constrain and are constrained by the network structure.
- The connectivity of a network as a whole depends on dynamical processes that operate at the local scale (such as rules that govern the appearance and connections of new vertices.
We move on to explore the structural dynamics nature's networks in more detail by considering pattern formation, changes that take place from within a pattern, changes that are driven by factors external to a pattern, and the size and scaling of patterns.
This document is a draft of work in progress. Please post your comments, thoughts, and suggestions:
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