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Pattern Formation

The flocking of birds and the schooling of fish in one of the most dynamic forms of pattern formation generated by the local interactions between the members

The flocking of birds and the schooling of fish in one of the most dynamic forms of pattern formation generated by the local interactions between the members

A pattern is any set of correlations between the states of elements within a system. Pattern formation refers to the process through which a coherent set of associations between element’s states is formed and persists over some period. A primary question we are interested in when studying any pattern is the question of how was it generated or formed? In answering this question, we can make a fundamental distinction between those patterns that were created through order being imposed by some other external organization, or those that were created through the pattern being internally generated.
The term pattern formation typically refers to internally generated patterns. By pattern formation, we mean that certain systems have the ability to self-organize into structured states from initially unstructured or homogeneous states. This internal pattern formation process is a universal phenomenon as it has been identified in physical, biological, economic and social systems.1 One primary characteristic of emergent pattern formation is the lack of centralized control. This process of emergent pattern formation uses only local dynamics to influence the system’s global behavior.2 No single part of the organization coordinates the macro-level behavior. Thus it is typically not possible to directly control the macro level pattern; it is only possible to effect the micro level parts.3 Some examples of emergent patterns include the ripple patterns in a sand dune created by wind or water.4 Swarming and flocking are a well-known emergent behavior in many animal and insect communities. The development of traffic patterns like gridlock, as well as the formation and adoption of new cultures, are internally generated patterns formed out of local interactions between the parts.

Feedback

A central characteristic of internally generated pattern formation is positive feedback. Positive feedback is a process whereby more begets more, i.e. the more we have of something the more we will get of it in the future. Compound interest is an example of positive feedback, the more money in an account, the more interest that will accrue, which will mean more money in the account in the future, which will feedback to generate more interest, etc.
Within pattern formation, positive feedback works to enable some small – possibly random – event to take hold within a system and get amplified into a global pattern. For example, we can see positive feedback at work in the formation of sand dunes. Wind flowing across the sand carries small grains of sand with it. Slight unevenness in the surface of the ground creates a greater likelihood of grains collecting at a high point, creating an accumulation that then increases the size of this small lump, which then feeds back to increase the likelihood of more grains collecting at this point. Over time a dune can form, but of course the dune can not go on building up forever, as it gets higher the sides get steeper and it becomes easier for grains to slide off. This is the negative feedback that places constraints on the pattern’s formation. The fully covered pattern of the dunes or wind ripples is the product of many of these dunes building up until they meet each other to create a complete pattern.

The same basic process of positive feedback that drive many forms of pattern formation create the striped pattern to zebras' skin

The same basic process of positive feedback that drives many kinds of pattern formation creates the striped pattern to zebras’ skin

Another example is the formation of convection cells within heated water. Convection cells emerge that transport the heat to the cooler regions near the surface of the liquid where the heat is given off. While at the same time cooled liquid is pushed to the bottom to be reheated creating a circular motion in the water and the formation of a pattern through the internal interaction between the warm and cool water.5 Similar patterns of hexagons and stripes can be found in very different physical and biological systems. For instance, these striped patterns are observed on the skin of zebras and on human fingerprints.6 Ant foraging is another example of pattern formation through positive feedback. There is no central organization within an ant colony; coordination is achieved through the exchange of chemical pheromones between the ants, directly ant to ant as a means of communication. When an ant finds a food source it will excrete a pheromone on its way back to the colony. Other ants then pick-up on this and follow the source, if they too find food they will also leave a pheromone trail. Thus a stronger scent will build up, feeding back to induce more ants to follow. This is again a form of positive feedback that has lead to the formation of the global pattern out of local interactions.
Another example within social organizations would be the development of open source projects. Many open source projects are initiated, but only a few become large scale stable patterns of organization like Wikipedia or WordPress; again this is a product of positive feedback. The more people that contribute to a project and the more people participating in using the system, the more promotion and exposure it will get and the more attractive it will become for others to joint.

Energy

In these above examples, one can note how it was in some way the energy that was being inputted to the system that enabled the internal pattern to form. Whether the wind moving the sand grains, the heat moving the water, the food for the ants, or people’s work and attention driving the social organization. Emergent pattern formation may be internally generated, but it typically requires some input of energy, and this can help us to understand why the process takes place. Often the elements in the system organize themselves to better intercept and transform the energy source – either randomly or purposefully. With many physical systems, this is somewhat random. With the accumulation of sand dunes, it was the random difference in the surface that enabled some areas to harness the wind’s force towards building up their structure. But in many biological systems, this process in less random and in social systems it can be entirely purposeful.
In these cases, there is a random arrangement of elements on one level, and there is some free energy source available within the environment, with the parts being only capable of intercepting that energy source through forming a particular global pattern. Any set of components that can form that particular pattern will then be able to access the energy, and this will create a positive feedback. Whereby the organization can get more energy and redistribute more to its constituent elements. This means more elements will be attracted to that configuration which will lead to the interception of more energy, etc. For example, we can understand evolution in this fashion. Many of the energy sources that creatures use are only accessible by many different parts coordinating their activities towards intercepting and transforming the resource. Examples would include photosynthesis and mammalian digestion. These activities take the coordination of millions of cells and tissues; in isolation, none of the parts would be able to intercept these energy sources.
This idea is also captured in the theory of symbiogenesis which propounds the idea that several essential organelles of eukaryote cells originated as a symbiosis between separate single-celled organisms.7 Different more rudimentary organizations combined to form more complex organisms that were then capable of differentiating their internal features towards achieving greater overall functionality and thus becoming potentially more prolific. For example, some coral can intercept and process light through photosynthesis by ingesting an alga that then forms part of the coral’s structure. The algae can be found in the tissues of the coral, producing food through photosynthesis which is then taken in by the coral and in return the host coral gives the algae a habitat.8

Environmental Adaptation

The organization of people into economic units to accomplish combined projects is an example of pattern formation in order to perform a function or intercept resources that none in isolation could access.

The organization of people into economic units to accomplish combined projects is an example of pattern formation in order to perform a function or intercept resources that none in isolation could access

This process of pattern formation can then be understood as a form of adaptation, a process whereby the system adapts to its environment. That is to say that emergent pattern formation is a process that involves the interaction between the system and its environment, whereby the parts of the system organize themselves in response to changes in the environment. In so doing we get the formation of higher level patterns to intercept new resources. For example, we can ask how did we get life from nonliving elements? From the perspective of physics, the primary difference between an inanimate composite of carbon atoms and a living system is that the latter can intercept and process energy within their environment; but to do this the parts have to be arranged in a particular fashion.
One formulation of this theory9 based on thermodynamic principles, posits that when a combination of atoms is driven by a source of external energy – such as the sun – and surrounded by a heated environment – such as the sea or atmosphere – the system will often slowly restructure itself so as to dissipate more energy over time. This may lead under certain conditions to inanimate matter over prolonged periods of time adopting key physical attribute associated with life. The MIT researcher, Jeremy England, who formalized a theory of this kind stated it directly when he said: “You start with a random clump of atoms, and if you shine light on it for long enough, it should not be so surprising that you get a plant.”10 A simple illustration of pattern formation within a social system can help to clarify the basic constituents of this process. Take ten beekeepers that all need to purchase sugar to feed their bees, but they each have a limited budget. If they each purchased in isolation, they would have to buy in individual packets from the local shop which would cost them too much to make it viable. If however, they formed some organization, they would be able to go to the distributor and purchase in bulk for the entire group at a discounted rate, making it a viable option. We can see in this illustration how under the initial condition where there was a lack of organization – i.e. pattern – they were not able to intercept the resources. But by forming some pattern of organization – i.e. communicate a plan, collect all the money, purchase the sugar and then distribute it; all of which would require significant organization – they were able to intercept the resources that made the overall organization more viable and capable of developing. This same process is pervasive throughout socio-economic systems, as social systems are not dependent upon randomness in this process of pattern formation, but with the cognitive capabilities of the individuals can identify and purposefully work towards higher levels of organization.

Cite this article as: Joss Colchester, "Pattern Formation," in Complexity Academy, August 17, 2016, http://complexityacademy.io/pattern-formation/.

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