This semester, I am taking a foundational class in the Systems Engineering department here at Cornell and I wanted to use this blog post to relay some cool packages and tools that we have used that hopefully can be useful teaching material for emerging faculty or anyone looking for interactive systems tutorials.
To begin, we have to first define what falls under the umbrella of complex adaptive systems. In a nutshell, these systems tend to (1) have networks of many components, (2) typically involve non-linear interactions between components, (3) exhibit self-organizing behavior, (4) have the potential to exhibit emergent properties. One really beautiful website that explains these properties in more detail is Complexity Explained, which started as a community outreach project to try to explain complex systems to a wider audience within the science community and the public. The website features interactive animations of systems properties and a short booklet that can be downloaded (in many languages) with key concepts.
It is well known that complex systems are hard for humans to understand because many of the characteristics are non-intuitive for us. For example, self-organizing behavior is often contradictory to our own lives (when can you remember a time that a system around you naturally seemed to become more orderly as time passed?). Emergent properties can come about in long time scales that are often far distanced from the original action. We can’t always understand how decisions on the microscale resulted in large macroscale processes. Thus, in order to best approach complex systems, we must have the ability to interact with them, model them, and map out their complex behavior under many conditions. Below, I am introducing some tools that might help foster more understanding of these ideas using simple, yet dynamically rich cases.
One of the main creators of the Complexity Explained website and a visiting lecturer to my systems class is Hiroki Sayama, a world-renowned researcher and director of the Center for Collective Dynamics of Complex Systems at Binghamton University. Dr. Sayama has created a python package called PyCX that contains sample Python codes of complex systems that a user can run interactively and then manipulate or build off of. Simply download the package off of GitHub and all of the code and a simulator will be available to you. Figure 1 shows an example interactive simulation of a Turing pattern. In 1952, Alan Turing authored a paper where he described how patterns in animals’ coats such such as stripes and spots, can arise naturally from a chaotic system. He uses a simple set of reaction-diffusion equations to describe this process. Figure 1 shows the python simulator in PyCX, the equation for the Turing pattern, and the evolution from the random initialization to the ordered spots.
PyCX also allows you to toggle the parameters of the problem, which can express how small perturbations in the system can lead to substantially different outcomes. You can adjust these parameters within the source python code (which I believe is more useful for students rather than just clicking a “play” button). Figure 2 shows the difference in behavior across a forest fire model when the initial density is adjusted from 35% to 40% of the space.
Golly- Game of Life Simulator
Golly is an open-source tool for visualizing cellular automata, including Conway’s Game of Life. Golly allows the user to draw different patterns and apply specific rules for how the systems evolve. You can stop the simulation midway and apply different rules to the existing patterns.
Dr. Sayama also developed a really interesting Java application to study swarm behavior, or collective behavior that is exhibited by entities, typically animals. This application, called swarm chemistry creates agents with different kinetic parameters that dictate dynamics. The application allows you to mix agents into a single population and observe how emergent dynamics form. Figure 4 shows the opening interface when you click the .jar executable. The application brings up 6 random agents that exhibit some dynamic behavior. By clicking on any two agents, you will create a new population that shows how the dynamics of the agents interact (Figure 5). You can keep mixing agents and adding more random swarms. You can individually mutate certain swarms or edit the parameters as well. The pictures do not do this application justice. It is super fun (and slightly addicting) and a great way to get students excited about the concepts.
I had so much fun using these packages in class and I hope that these tools can help you/your students become more engaged and excited about complex systems!
My knowledge of these tools came from Hiroki Sayama’s guest lectures in SYSEN 6000 at Cornell University and from:
Sayama, H. (2015) Introduction to the Modeling and Analysis of Complex Systems,Open SUNY Textbooks, Milne Library, State University of New York at Geneseo.