 As we've talked about in a previous module, a pattern is any set of correlations between the states of elements within a system. The term pattern formation then refers to the process through which this coherent set of associations between the elements states is formed and persists over some period of time. It captures the essence of self-organization and emergence in all kinds of systems. A primary question we're interested in when studying any pattern is the question of how is it generated or formed. In answering this question we can make a fundamental distinction between those patterns that were created through organization being imposed by some 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 phenomena as it has been identified in physical, biological, economic and socio-cultural systems. One primary characteristic of emergent pattern formation is the absence of centralized control regulating the process. This process of emergent pattern formation uses only local dynamics to influence the system's global behavior. No single part of the organization coordinates its macro-level behavior. Thus it is typically not possible to directly control the macro-level pattern. It is only possible to affect the micro-level parts in their interactions. Some examples of emergent patterns include the ripple patterns in a sand dune created by wind or water. Swarming and flocking are 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 all internally generated patterns that form out of the local interactions between the parts. A central characteristic of internally generated patterns is positive feedback. Positive feedback is a process whereby more begets more. That is to say, the more we have of something, the more we will get of it in the future. Compound interest on a bank account is an example of positive feedback. The more money in the account, the more interest that will accrue, which will result in there being more money in the account in the future, which will feedback to generate more interest etc. With pattern formation, this 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. Light unevenness in the surface of the ground creates a greater likelihood of grains at that high point of resistance, 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. In this way, over time, a sand dune can form, but of course the sand dune cannot 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 sand dunes or wind ripples is the product of many of these dunes building up until they meet each other to create a complete pattern. Another example is the formation of convection cells within heated water. Convection cells in the water emerge that transport the heat to the cooler regions near the surface of the liquid where the heat is then given off, while at the same time cooled liquid is pushed to the bottom to be reheated, in so doing creating a circular motion in the water and the formation of a pattern through the internal interaction between the warm and cold water. Similar patterns of hexagons and stripes can be found in very different physical and biological systems. For instance, similar striped patterns are observed on the skin of zebra and on human fingertips. Ant foraging is another example of pattern formation through positive feedback. There is no centralized organization within an ant colony. The high level of coordination is achieved through the exchange of chemical pheromones between 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 over time a stronger scent will build up, feeding back to induce more ants to follow. This is again a form of positive feedback that is led to the formation of the global pattern out of local interactions. Another example within social systems will 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 participating in using the system, the more promotion and exposure it will get and the more attractive it will become for others to join. In all of these 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 it was 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 in understanding 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. In many physical systems, this is a somewhat random process. 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. Within many biological systems, this process is 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 the particular pattern will then be able to access the energy and this will create positive feedback, whereby this particular organization can get more energy and thus redistribute more to its constituent elements. This means that more elements will be attracted to that configuration, which will lead to the interception of more energy etc., a positive feedback. 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 that resource. Examples would include photosynthesis within plants 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 eukaryotic cells originated as a symbiosis between separate single-celled organisms. Different more rudimentary organisms combine to form more complex organisms that were then capable of differentiating their internal features towards achieving greater overall functionality and thus becoming potentially more successful and prolific. For example, some coral can intercept and process light through photosynthesis by ingesting an algae that then forms part of the coral 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. 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 as a combined organization. For example, we can ask how do we get life from non-living 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 environments. But to do this, the parts have to be arranged in a particular fashion. There must be synergies between them. One formulation of this theory, based on thermodynamic principles, posits that when a combination of atoms is driven by a source of external energy such as sunlight 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 attributes associated with living systems. The MIT researcher Jeremy England who formalized a theory of this kind stated it directly when he said quote, 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. A simple illustration of pattern formation within a social system can help us to clarify the basic constituents of this process. There are like 10 beekeepers that all need to purchase sugar to feed their bees but they each have only a limited budget. If they each purchase 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 one organization they would be able to go directly to the distributor and purchase in bulk for the entire group at a discount rate making a viable option for all. We can see in this illustration how under initial conditions where there was a lack of organization that is to say pattern they were not able to intercept the resources but by forming some pattern of organization that is to say communicating a plan, collecting all the money, purchasing the sugar and then distributing it all of which would require significant organization. They were able to intercept the resources that made the organization more viable and capable of developing. This same process is pervasive throughout socioeconomic 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.