Compression-Based Investigation of the Dynamical Properties of Cellular Automata and Other Systems

Hector Zenil, Laboratoire d'Informatique Fondamentale de Lille, Institut d'Histoire et de Philosophie des Sciences et des Techniques
2010 Complex Systems  
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 compression-based approach classifies cellular automata into clusters according to their heuristic behavior. These clusters show a correspondence with Wolfram's main classes of cellular automata behavior. A Gray code-based numbering scheme is developed for
more » ... ing initial conditions. A compression-based method to estimate a characteristic exponent for detecting phase transitions and measuring the resiliency or sensitivity of a system to its initial conditions is also proposed. A conjecture regarding the capability of a system to reach computational universality related to the values of this phase transition coefficient is formulated. These ideas constitute a compression-based framework for investigating the dynamical properties of cellular automata and other systems. Complex Systems, 19
doi:10.25088/complexsystems.19.1.1 fatcat:6vgn44ih5ncqzjxixsxhq6gnba