The GraftalLace Cellular Automaton

TL;DR

The paper introduces the GraftalLace Cellular Automaton (GLCA), a new 1D cellular automaton that generates complex fractals and patterns through bitwise influence rules, with potential 2D extensions resembling Conway's Game of Life.

Contribution

It presents a novel cellular automaton model that produces symmetric fractals and complex patterns, including reversible rules and 2D representations.

Findings

Generation of Sierpinski and Pascal fractals

Discovery of reversible rules for GLCA

Potential for 2D tessellation and complex pattern extension

Abstract

We introduce our GraftalLace Cellular Automaton in short GLCA which is a new one-dimensional cellular automaton on the regular square lattice. It makes a monochromatic infinite directed graph otherwise an octal number triangle or number trapezoid by partly influences the states of the neighbour cells with bit operations. We show new ways to make symmetric fractals like Sierpinski triangle and Pascal triangle modulo 3 and unknown complex patterns. We find reversible rules and show possibilities to represent and extend our automaton in different ways. 2D version of GLCA can be represented as a 3D digraph or a 2D animated tessellation which could be a closer relative of Conway's Game of Life.