Generating Patterns on the Triangular Grid by Cellular Automata including Alternating Use of Two Rules

Abstract

Various patterns and figures are used widely in image processing including tests of various algorithms, compressing images and also creating/displaying them in computer games. In this paper binary image generation is studied on the triangular grid. On the one hand, the triangular grid has better symmetric properties than the square grid, while on the other hand, the number of closest neighbors of a pixel is less than it is on the square grid. In this way, cellular automata based on the closest neighbors are simpler than similar automata on the square grid, but the generated pictures may be more sophisticated. In our binary cellular automata the state (color) of the closest three neighbors and the pixel's own state determine the next state; we use life-like deterministic cellular automata. In our novel approach we combine two different automata (rules) such that we use them alternately for the picture generation. Various patterns, including highly symmetric mandala type patterns, as well as, airplanes, trees etc. are shown as examples. Some general ideas and hints are also given.