# Deformed Cellular Automata

## Mentor 1

Jeb Willenbring

## Location

Union Wisconsin Room

## Start Date

24-4-2015 2:30 PM

## End Date

24-4-2015 3:45 PM

## Description

Consider a large rectangular grid, like a sheet of graph paper. Next, imagine that a small computer is placed on each square box (i.e. cell). Assume that each of the computers on this grid takes its input from the computers surrounding it. This computational paradigm is called a cellular automata (CA). The most well-known example of CA is John Conway’s Game of Life in which cells evolve using simple rules in discrete time steps. The properties of this particular CA are quite well known and there are many variations of this game as well. / / Through our research we have constructed a new game we call a deformed cellular automata. Essentially this new game is two different games played simultaneously. The first is a standard Game of Life using the original rules proposed by Conway. In terms of a function the Conway rules produce results which are highly non-linear. The second is similar but uses continuous time steps and a different set of rules known as the voter model. We have found that this set of rules produces characteristics similar to a harmonic function. Together we blend these two games using a deformation rate, d. For example, when d=0 the game will behave entirely like the Game of Life. However, when d=1 the game will behave entirely like the voter model. Between 0 and 1 the game will exhibit new properties similar to some combination of both games. /

Deformed Cellular Automata

Union Wisconsin Room

Consider a large rectangular grid, like a sheet of graph paper. Next, imagine that a small computer is placed on each square box (i.e. cell). Assume that each of the computers on this grid takes its input from the computers surrounding it. This computational paradigm is called a cellular automata (CA). The most well-known example of CA is John Conway’s Game of Life in which cells evolve using simple rules in discrete time steps. The properties of this particular CA are quite well known and there are many variations of this game as well. / / Through our research we have constructed a new game we call a deformed cellular automata. Essentially this new game is two different games played simultaneously. The first is a standard Game of Life using the original rules proposed by Conway. In terms of a function the Conway rules produce results which are highly non-linear. The second is similar but uses continuous time steps and a different set of rules known as the voter model. We have found that this set of rules produces characteristics similar to a harmonic function. Together we blend these two games using a deformation rate, d. For example, when d=0 the game will behave entirely like the Game of Life. However, when d=1 the game will behave entirely like the voter model. Between 0 and 1 the game will exhibit new properties similar to some combination of both games. /