Touching Loop Patterns with Cellular Automata

TL;DR

This paper presents a cellular automata rule capable of generating stable, touching loop patterns on a 2D grid, using template matching and noise injection to evolve complex loop structures.

Contribution

It introduces a novel CA rule that forms touching loop patterns through systematic template matching and controlled evolution.

Findings

Successfully evolved stable touching loop patterns

The rule covers 2D space with overlapping tiles

Template matching guides pattern formation

Abstract

The objective is the design of a Cellular Automata rule that can form patterns with 'touching' loops. A loop is defined as a closed path of 1-cells in a 2D grid on a zero background and with a zero border. A path cell is connected with two of its adjacent neighbors. In touching loops a path cell is also allowed to touch another on a diagonal. A CA rule was designed that can evolve stable touching loop patterns. The rule tries to cover the 2D space by overlapping tiles. The rule uses so-called templates, 5 x 5 matching patterns which are systematically derived from the given set of 3 x 3 tiles. The rule checks the pattern being evolved against a list of templates. If the outer neighbors of a template match, then the cell's state is set to the template's center value. Noise is injected if there is no matching template, or the tiles are not properly assembled. Thereby the evolution is driven to the desired loop patterns.