Compression-based investigation of the dynamical properties of cellular automata and other systems

Hector Zenil (1)

1 IHPST - Institut d'Histoire et de Philosophie des Sciences et des Techniques

A method for studying the qualitative dynamical properties of abstract computing machines based on the approximation of their program-size complexity using a general lossless compression algorithm is presented. It is shown that the compressionbased approach classifies cellular automata (CA) into clusters according to their heuristic behavior, with these clusters showing a correspondence with Wolfram's main classes of CA behavior. A Gray code-based numbering scheme for initial conditions and a compression based method to estimate a characteristic exponent to detect phase transitions and measure the resiliency or sensitivity of a system to its initial conditions is also proposed, constituting a compression-based framework for investigating the dynamical properties of cellular automata and other systems.

Mots clés: cellular automata classification; Wolfram's four classes; phase transition detection; program-size complexity; compression-based clustering; non-linear dynamics; Lyapunov characteristic exponents; initial conditions enumeration

Domaines: Histoire, Philosophie et Sociologie des sciences

Hector Zenil. Compression-based investigation of the dynamical properties of cellular automata and other systems. Complex Systems , 2010, 19 (1), pp.1-28. ⟨halshs-00792118⟩