Cellular Automata in the Triangular Grid

Cellular automata are parallel computing devices working on a discrete timescale. Each cell of a regular grid has a finite number of states and the state in the next time instant depends only on the actual state of the cell itself and the states of its neighbor cells. When every cell could have exactly two states, they can be identified as “live” and “dead” states. “Game of Life” is a very popular type of cellular automata on the square grid based on the 8 neighborhood of the cells. There are various initial configuration that leads to periodic or growing or moving patterns, etc. Triangular Grid which also called an isometric grid, is a grid generated by tiling the plane regularly with equilateral triangles. In the thesis, life like cellular automata are analyzed in the triangular gird based on 3-neighborhood relation that is the next state of a cell depends only on its actual state and the states of its closest neighbor cells. There are 2 sets of conditions. The first set is called “Birth” or “B” which shows the number of live cells needed in the neighborhood of a dead cell to make it alive. The second set is called “Stay alive” or “S” which shows the number of live cells needed in the neighborhood of a live cell to keep it alive. Various B/S models are analyzed. While some can generate patterns like snowflake or etc, some can be used for noise removal in image processing. Keywords: Cellular Automata, Game of Life, Triangular Grid