# Emergence: Fireflies

Emergence is one of the most intriguing phenomena in systems research. What is it? How can we use it? Here is an app toy I made to help understand the idea.

One of the most intriguing phenomena within complexity science is that of emergence.  It is a salient feature of complex systems, so much so that definitions of complex systems include the quality of exhibiting emergence.  Many exciting solutions to the world’s bigger problems can be understood through collective dynamics and emergence.

Google’s search algorithm, to a heavy extent, depends on the nature of linking between websites.  On the scale of the website and what links to it, Google is able to provide an answer the global problem of findability on the internet.

Muhammad Yunus developed a micro loan system that re-frames loans to take into account collective dynamics of a group.  Through challenging the assumption of who one can give a successful loan to, and by tapping into group trust, he has created an effective method of alleviating poverty.

What is Emergence?

Simply put, emergence is when behavior at a smaller scale of a system produces global behavior that is not entirely intuitive given the behavior at the smaller scale.  The global behavior is not directly programmed in the behavior at the local level. Something surprising happens at the larger scale.  From simple local interactions, we can arrive at global behavior that is immensely complex, sometimes seemingly random. Think of the classic example of Conway’s Game of Life. The rules to define the simulation are simple, but the behavior can be pretty unpredictable. Or on the other hand, we can think of systems which have a lot of randomness at the smaller scale, but order emerges at the larger scale. This underlies the concept of self-organization, a process which is widespread in the development of biological and societal form.

Another way to think of emergence involves the notion that the whole is greater than the sum of its parts. The behavior of the system is a result of not only its parts, but their interactions. The actions at the level of the individual do not imply that of the behavior of the system. We need to understand not only the system at the individual level, but at the level of multiple individuals to observer the effect of their interactions. One of the most exciting examples of emergence involves evolution. At a smaller scale we have natural selection, species in a population surviving or dying over time based on selection pressures from the environment, with possible species variations through reproduction and sexual selection and the random chance of mutation. At a larger scale we have the development of biodiversity, a wide range of organisms from bacteria to whales, and an environment with so many different species able to thrive within different niches. Global biodiversity is not programmed in the local interactions; it is an emergent property.

Why is it important?

Understanding emergence is essential when working with complex systems. For the most part, complex systems exist because they are grown, i.e. they have evolved to be what they are. Think about what makes up a complex system. They are composed of many parts that interact across scales, from individuals to groups to the whole. When you think of a city, it grows through the interaction of all of the individuals and organizations which comprise the city. The city is not formed by a single individual, it is formed by its population. Emergent behavior can be difficult to understand, since by its very nature it is unintuitive and unpredictable (the very reason why it has received so much attention). In understanding global behaviors of a system, it helps to understand how individual interactions led to the global behaviors. In this way, one can attempt to reproduce the global behaviors through recreating the individual interactions.

Example of Emergent Behavior: Fireflies

A popular example which illustrates emergent phenomena is that of fireflies which can spontaneously synchronize. There is no head firefly with the ability to communicate with all of the others, so how is it possible that they can flash in synchrony, when no firefly can see all of the rest? In their paper ‘Synchronization of pulse-coupled biological oscillators’, R. Mirollo and S. Strogatz seek to answer this question by developing a model that introduces a mechanism of simple interactions between the fireflies. Through this local interaction, the global behavior is that of synchrony. The key concept with respect to emergence is that the local interactions do not mention anything about synchronizing. Each firefly can be thought of as an oscillator which fires at time T, and resets to zero only to fire again at time T. All of the fireflies have the same period T, but start at different times in their period. At each step, all of the fireflies increment in their period. A firefly has the ability to see neighbors within a certain detection radius. When one of the neighbors of a firefly flashes, the firefly increments in its period, leading it closer to flashing. The nature of this firing response is important. Say that a firefly is at time t’ in its period. The firing response is defined as follows: the amount of increment increases as t’ increases. So if a firefly is later in its period, the increment will be higher. If its just beginning its period, the increment will be lower. The next is not so important for the concepts, but mathematically it can be more accurately stated as such:
$t''=f^{-1}(f(t')+\varepsilon )$
Here, t” is the new internal time if a firefly experiences a flash at time t’. As defined in the model, f is the firing function and epsilon is a small constant < 1 .
From these specifications, the fireflies will synchronize. The synchronization can be viewed in the following applet. I approximate the increment function as described in the paper ‘Fireﬂy-Inspired Sensor Network Synchronicity with Realistic Radio Effects‘ Werner-Allen, et. al. as

$\Delta t=\varepsilon t$

Where epsilon is 0.1 .

Click on the image to see the simulation

The simulation is done in Processing. I encourage you to open it up and play with the number of fireflies and the period.
It is difficult to really see where in the period each firefly is, so I created another model which simulates the fireflies as if they are standing in a single line. They bounce up and down periodically, flashing when they hit the ground. If a neighbor flashes, they increment in their period, evident in a sharp jump. This one has an interface to allow you to change the number of fireflies, the period, and the detection radius (how far a firefly will look to its left and right to detect a neighbor.

Click on the image to see the simulation. This one includes an interface to play with!

Its pretty exciting to see the simulation converge to synchrony. From a simple rule given a neighbor flashing, organization emerges as the fireflies flash as a group. The group is able to act as a whole through local interactions.

Cool! … now what?

Think about environments that your are in or have seen, and reframe them in the systems perspective. How do the parts combine to form the whole. Is the emergent behavior obvious given local interactions?

What if there is a particular global quality you want to achieve. What are ways in which local interactions can achieve those global qualities? Because the global behavior can be unpredictable, it can become a difficult problem to determine the local interactions. But other times, those interactions can be found through the ingenuity of a group and global behaviors can be achieved. The question then also becomes, how do you create and environment that will promote such creativity? This is a question of emergence, in designing local interactions to promote global creativity.

Design and Dissemination

An example of the utility of thinking in terms of systems and emergence is in the world of creativity and design. If a designer and the consumer have similar environments, it is very likely the designer can find successful solutions for the consumer. In cases where the designer and the user are in completely different environments (including different experiences and customs), it will be immensely difficult for the designer to make something useful. In some cases, products will be developed, only to suffer completely different uses in the field (which is not always bad, but it is a gamble). So if instead the designer works with the user, together they can design something successful. From the complex process of improving experiences through design, the collaboration leads to the emergence of successful, effective solutions. This may appear intuitive, but it has not always been the case that those who believe they have solutions have taken the time to fully understand to conditions those who they are trying to help.

With respect to dissemination, the goal is to have emergent behavior that spreads information, or a product. The question becomes: what sort of local interactions will result in this global goal? There are many ways to approach this problem, but a few methods include understanding the topology of the society in disseminate within. Certain people are more likely to spread information or a product, so if one targets those people, the product will spread faster and further. Another approach is to focus on the role of the individual. If one is empowered to be included in the product design and construction, they will not only help in characterizing the problem, but will have a deeper connection with the product. It is more likely they will, in their enthusiasm and success, spread the information and product to others. The task becomes including those who use the product to become part of the design process, be it through business, construction, or design, and they will in their own interests spread the product.

An apt analogy is to think of the process of gardening and growth. The designer is a seed, and the soil are those who will use the product in whatever environment they are in. The soil contains the nutrients, that which the seed needs to form into a healthy plant. From the interaction of the two, a product is formed, the plant. Though the seed may be the same, in two different environments, the plant will be different. From the environment of collaboration, many solutions are possible. Such solutions may spawn more seeds that in turn develop more solutions.

This process is not too difficult to grasp. What becomes harder to fathom is the type of solutions developed in the aggregate. The variety of solutions and even ideas for possible solutions of the group far surpass that of the individual. It becomes difficult to predict the creative capabilities that emerge in a group.

Collectively we are capable of much more than any of us alone can imagine.

The above article describing emergence was created as a supplement for Eric Reynold’s presentation on creative capacity building and systems science at the 2010 International Development and Design Summit in Fort Collins, Colorado.