Algorithmic Information Dynamics of Persistent Patterns and Colliding Particles in the Game of Life

We demonstrate the way to apply and exploit the concept of \textit{algorithmic information dynamics} in the characterization and classification of dynamic and persistent patterns, motifs and colliding particles in, without loss of generalization, Conway's Game of Life (GoL) cellular automaton as a case study. We analyze the distribution of prevailing motifs that occur in GoL from the perspective of algorithmic probability. We demonstrate how the tools introduced are an alternative to computable measures such as entropy and compression algorithms which are often nonsensitive to small changes and features of non-statistical nature in the study of evolving complex systems and their emergent structures.

[1]  V. Benci,et al.  Dynamical systems and computable information , 2002, cond-mat/0210654.

[2]  Jean-Paul Delahaye,et al.  An Algorithmic Information Theoretic Approach to the Behaviour of Financial Markets , 2010, ArXiv.

[3]  Hector Zenil,et al.  Algorithmic Data Analytics, Small Data Matters and Correlation versus Causation , 2013, 1309.1418.

[4]  A. Kolmogorov.  Three approaches to the quantitative definition of information , 1968 .

[5]  Jean-Paul Delahaye,et al.  On the Algorithmic Nature of the World , 2009, ArXiv.

[6]  Jean-Paul Delahaye,et al.  Correspondence and Independence of Numerical Evaluations of Algorithmic Information Measures , 2012, Comput..

[7]  Dennis Saleh.  Zs , 2001 .

[8]  Gregory J. Chaitin,et al.  On the Length of Programs for Computing Finite Binary Sequences: statistical considerations , 1969, JACM.

[9]  Allen H. Brady.  The determination of the value of Rado’s noncomputable function Σ() for four-state Turing machines , 1983 .

[10]  Hector Zenil,et al.  Natural scene statistics mediate the perception of image complexity , 2014, ArXiv.

[11]  Hector Zenil,et al.  A Computable Measure of Algorithmic Probability by Finite Approximations , 2015, Complex..

[12]  Ming Li,et al.  An Introduction to Kolmogorov Complexity and Its Applications , 2019, Texts in Computer Science.

[13]  Jean-Paul Delahaye,et al.  Two-Dimensional Kolmogorov Complexity and Validation of the Coding Theorem Method by Compressibility , 2012, ArXiv.

[14]  Paul M. B. Vitányi,et al.  The miraculous universal distribution , 1997 .

[15]  Hector Zenil,et al.  An Algorithmic Information Calculus for Causal Discovery and Reprogramming Systems , 2017, bioRxiv.

[16]  Hector Zenil,et al.  Correlation of automorphism group size and topological properties with program−size complexity evaluations of graphs and complex networks , 2013, 1306.0322.

[17]  Hector Zenil,et al.  Algorithmic Complexity of Financial Motions , 2014 .

[18]  Hector Zenil,et al.  A Decomposition Method for Global Evaluation of Shannon Entropy and Local Estimations of Algorithmic Complexity , 2016, Entropy.

[19]  Genaro Juárez Martínez,et al.  A Computation in a Cellular Automaton Collider Rule 110 , 2016, ArXiv.

[20]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[21]  Nicolas Gauvrit,et al.  Structure emerges faster during cultural transmission in children than in adults , 2015, Cognition.

[22]  Hector Zenil,et al.  Methods of information theory and algorithmic complexity for network biology. , 2014, Seminars in cell & developmental biology.

[23]  Jean-Paul Delahaye,et al.  Calculating Kolmogorov Complexity from the Output Frequency Distributions of Small Turing Machines , 2012, PloS one.

[24]  Hector Zenil,et al.  Low Algorithmic Complexity Entropy-deceiving Graphs , 2016, Physical review. E.

[25]  A. Blokhuis.  Winning ways for your mathematical plays , 1984 .

[26]  Hector Zenil,et al.  Coding-theorem like behaviour and emergence of the universal distribution from resource-bounded algorithmic probability , 2017, Int. J. Parallel Emergent Distributed Syst..

[27]  T. Rado.  On non-computable functions , 1962 .

[28]  Hector Zenil,et al.  Algorithmic complexity for psychology: a user-friendly implementation of the coding theorem method , 2016, Behavior research methods.

[29]  Jean-Paul Delahaye,et al.  Human behavioral complexity peaks at age 25 , 2017, PLoS Comput. Biol..

[30]  Master Gardener,et al.  Mathematical games: the fantastic combinations of john conway's new solitaire game "life , 1970 .