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Wolfram Summer SchoolFounded in 2003

17th Annual Wolfram Summer School, held at Bentley University June 23–July 12, 2019


Sahand Hariri Akbari

Class of 2008


Sahand Hariri Akbari is currently working on his master's in mechanical engineering at Temple University.

Project: Searching for Circular Patterns in 2D CA

Most of the two-dimensional cellular automata generate square patterns. Few have been discovered that are able to approximate a circle (NKS pp. 177, 178). The objective of this project is to look for two-dimensional cellular automata that generate circular patterns.

Finding circular patterns requires devising an automated scheme to recognize circular shapes and performing an exhaustive search through the rule space. The examples provided in the NKS book are 9-neighbor totalistic cellular automata. Considering the extensive size of the rule space (totalistic and non-totalistic), one needs to limit the search to a subset of the rule space. A good initial step might be implementation of two-dimensional cellular automata on grids of hexagons as opposed to squares. In this layout, each cell has 6 neighbors, resulting in considerable reduction of the size of the rule space. Additionally, intuition suggests hexagonal grids may be able to generate circular patterns more easily than rectangular grids.

This project is then divided into two parts. The first part is to implement two-dimensional cellular automata on hexagonal grids, and the second part is to formulate filters for recognizing circular patterns.

Favorite Radius 3/2 Rule

Rule 39316