Touching Loop Patterns with Cellular Automata

Fuente: arXiv
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Main Author: Hoffmann, Rolf
Format: Preprint
Published: 2024
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author Hoffmann, Rolf
author_facet Hoffmann, Rolf
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2410_13425
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Touching Loop Patterns with Cellular Automata
Hoffmann, Rolf
Cellular Automata and Lattice Gases
Geometric Topology
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.
title Touching Loop Patterns with Cellular Automata
topic Cellular Automata and Lattice Gases
Geometric Topology
url https://arxiv.org/abs/2410.13425