Aspects of first and second order cellular automata

Abstract

An introduction to the field of Higher-Order Cellular Automata (HOCA) is provided. Key concepts are defined and illustrated using examples. Some of the possibilities offered by this framework are explored, and used to take a new look at old problems. A music-generating automaton is introduced, using higher-order morphology to include music theoretical aspects in the structure. Self-Organization is studied through the use of two higher-order extensions of well-known models; the Sandpile model, and Birth/Survival games. A dynamic lattice extension of the HOCA framework is also suggested. This is used to generate fractal shapes, and to estimate fractal dimensions.