# Fernando Sánchez Castellanos Villafuerte

Summer School

Class of 2011

## Bio

I have recently graduated with a bachelor’s degree from the computer science program at the Universidad de Guanajuato and I will be pursuing a masters in computer science at the Centro de Investigación en Matemáticas.

My interests are game theory, algebra, and microeconomics. I like to use math and computer programming to solve everyday problems.

I enjoy reading Middle Eastern literature and watching films.

## Project: Rules Based on Group Multiplication Tables

My project is to explore the rules that are based on group operations and how the properties of said operations (abelian, cyclic, and generators) affect them and define their behavior. Some of the rules based on non-commutative groups can behave in a class 3 way, given the proper initial conditions, which I believe are closely related to the generators of the group and their orders. The first step I’m taking toward understanding this behaviour is to plot rules based on simple non-commutative groups (S_3,S_4,D_4,…) given initial conditions {{i,j},k} with 0=<i,j,k=<GroupOrder[group] and to try to determine which of them produce a class 3 behaviour. Hopefully, I will be able to claim what are the required and needed properties of the initial conditions that produce class 3 behaviour. Further steps in this project include the search for class 4 behaviour and understanding the role subgroups have and the relation between the rules produced by two groups and the one by their direct product.

## Favorite Four-Color Totalistic Cellular Automaton

Rule 320740

• 22nd Annual Wolfram Summer School
• Bentley University, Waltham, MA, USA
• June 23–July 11, 2024