Dynamical systems with nonlocal connections have potential applications to economic and biological systems. This paper studies the dynamics of nonlocal cellular automata. In particular, all two-state three-input nonlocal cellular automata are classified according to the dynamical behavior starting from random initial configurations and random wirings; although it is observed that sometimes a rule can have different dynamical behaviors with different wirings. The nonlocal cellular automata rule space is studied using a mean-field parametrization which is ideal for the situation of random wiring. Nonlocal cellular automata can be considered as computers carrying out computation at the level of each component. Their computational abilities are studied from the point of view of whether they contain many basic logical gates. In particular, I ask the question of whether a three-input cellular automaton rule contains the three fundamental logical gates: two-input rules AND and OR, and one-input rule NOT. A particularly interesting “edge-of-chaos ” nonlocal cellular automaton, the rule 184, is studied in detail. It is a system of coupled “selectors ” or “multiplexers”. It is also part of the Fredkin’s gate — a proposed fundamental gate for conservative computations.

This paper will review electronic music and sonic art applications of Cellular Automata (CA) in a historical and technical context. Algorithmic and computational processes have been of interest to artists for many years, creating an emerging culture of generative electronic art. Creating patterns and sequences is necessary for the creative artist working spatially and temporally within a chosen medium. CA are capable of a wide variety of emergent behaviours and represent an important generative tool for the artist. The sonic artist and musician must be prepared to investigate the theoretical background of CA in order to successfully employ their vast behaviour space within compositional strategy. There is an extensive amount of mathematical and scientific literature relating to CA, however much of this is esoteric or difficult to understand. Important and accessible CA concepts are presented concisely in a non mathematical context to give sufficient background for the review. There have been several approaches at applying CA in the production of electronic music and sonic art. Examples exist in the fields of overall structural composition, MIDI sequencing and sound synthesis/modification techniques. Applications from academic, independent and commercial sectors will be critically reviewed in an artistic, historical and technical context. This will provide the artist and scientist with a balanced view of this emerging field.

Abstract. This paper describes a model of three-dimensional cellular automata allowing to simulate different phenomena in the fields of computer graphics and image processing, and to combine them together in order to produce complex effects such as automatic multitexturing, surface imperfections, or biological retina multi-layer cellular behaviours. Our cellular automaton model is defined as a network of connected cells arranged in a natural and dynamic way, which affords multi-behavior capabilities. Based on cheap and widespread computing systems, real-time performance can be reached for simulations involving up to a hundred thousand cells. Our approach efficiency is illustrated through a set of CA related to computer graphics –e.g. erosion, sedimentation, or vegetal growing processes – and image analysis –e.g. pipeline retina simulation. Key words: cellular automata, geometric modelling, image processing, environmental and biological systems, surface effects, fluid simulation 1