Diego Gutierrez Coronel graduated summa cum laude in May 2018 with a BS in physics and a minor in applied mathematics from the Illinois Institute of Technology. He did undergraduate research in nonlinear optics and laser physics at Argonne National Laboratory as a Lee Teng Intern. He also assisted a research group at Illinois Tech working on photocathode materials for particle accelerators. Diego is a Colombian student interested in computation, mathematics and quantum physics. Besides his interests, he loves playing soccer (football) and running outdoors. He also likes traveling and reading.
Project: Implementing Cellular Automata for Arbitrary Regions
We attempted to generate a certain type of boundary conditions, such as those in partial differential equations, to apply cellular automata (CA) rules in regions contained by arbitrary boundaries. These boundaries could be irregular and may interact with the units inside. Two cellular automata were studied in particular, a simple forest fire model as a probabilistic CA and fluid flow as a hexagonal CA.
Main Results in Detail
Conway’s Game of Life CA was implemented to arbitrary regions defined by an image or different values on an array. Code from two Demonstration projects was modified to study two simple models. One was a forest fire and the other was fluid flow on arbitrary regions with a particular set of rules. These resulted in more applicable and interesting cellular automata.
Some studies of these types of boundary conditions have been done for Boolean CA; however, studying in more detail these kinds of boundary conditions can result in more interesting cellular automata. Just like for partial differential equations, one could classify these types of boundary conditions for CA. Other types of boundary conditions could be constructed and studied. For instance, one could construct a 2D cellular automata in the surface of a sphere or torus by setting certain transformations and periodic boundary conditions.