Evolving Structures in Complex Systems

In this paper we propose an approach for measuring growth of complexity of emerging patterns in complex systems such as cellular automata. We discuss several ways how a metric for measuring the complexity growth can be defined. This includes approaches based on compression algorithms and artificial neural networks. We believe such a metric can be useful for designing systems that could exhibit open-ended evolution, which itself might be a prerequisite for development of general artificial intelligence. We conduct experiments on 1D and 2D grid worlds and demonstrate that using the proposed metric we can automatically construct computational models with emerging properties similar to those found in the Conway’s Game of Life, as well as many other emergent phenomena. Interestingly, some of the patterns we observe resemble forms of artificial life. Our metric of structural complexity growth can be applied to a wide range of complex systems, as it is not limited to cellular automata.

[1]  John von Neumann,et al.  Theory Of Self Reproducing Automata , 1967 .

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

[3]  Abraham Lempel,et al.  On the Complexity of Finite Sequences , 1976, IEEE Trans. Inf. Theory.

[4]  Stephen Wolfram,et al.  Universality and complexity in cellular automata , 1983 .

[5]  C. Langton.  Self-reproduction in cellular automata , 1984 .

[6]  S. Wolfram,et al.  Two-dimensional cellular automata , 1985 .

[7]  Charles H. Bennett.  Logical depth and physical complexity , 1988 .

[8]  Christopher G. Langton,et al.  Computation at the edge of chaos: Phase transitions and emergent computation , 1990 .

[9]  Thomas S. Ray,et al.  An Approach to the Synthesis of Life , 1991 .

[10]  Wentian Li,et al.  Transition phenomena in cellular automata rule space , 1991 .

[11]  Karl Sims,et al.  Evolving virtual creatures , 1994, SIGGRAPH.

[12]  Jürgen Schmidhuber,et al.  Sequential neural text compression , 1996, IEEE Trans. Neural Networks.

[13]  L. Yaeger.  Computational Genetics, Physiology, Metabolism, Neural Systems, Learning, Vision, and Behavior or PolyWorld: Life in a New Context , 1997 .

[14]  Alexei A. Efros,et al.  Texture synthesis by non-parametric sampling , 1999, Proceedings of the Seventh IEEE International Conference on Computer Vision.

[15]  Matthew V. Mahoney,et al.  Fast Text Compression with Neural Networks , 2000, FLAIRS Conference.

[16]  Alastair Channon,et al.  Improving and still passing the ALife test: component-normalised activity statistics classify evolution in geb as unbounded , 2002 .

[17]  L. Booker.  Perspectives on adaptation in natural and artificial systems , 2004 .

[18]  Charles Ofria,et al.  Avida , 2004, Artificial Life.

[19]  Lee Spector,et al.  Division blocks and the open-ended evolution of development, form, and behavior , 2007, GECCO '07.

[20]  Taras Kowaliw,et al.  Measures of complexity for artificial embryogeny , 2008, GECCO '08.

[21]  Hector Zenil,et al.  Compression-Based Investigation of the Dynamical Properties of Cellular Automata and Other Systems , 2009, Complex Syst..

[22]  Eleonora Bilotta,et al.  Artificial Micro-Worlds Part I: a New Approach for Studying Life-like Phenomena , 2011, Int. J. Bifurc. Chaos.

[23]  Jean-Paul Delahaye,et al.  Image characterization and classification by physical complexity , 2010, Complex..

[24]  Hector Zenil,et al.  What Is Nature-Like Computation? A Behavioural Approach and a Notion of Programmability , 2012, Philosophy & Technology.

[25]  P. Grassberger.  Randomness, Information, and Complexity , 2012, 1208.3459.

[26]  Hector Zenil,et al.  Asymptotic Behavior and ratios of Complexity in Cellular Automata , 2013, Int. J. Bifurc. Chaos.

[27]  Kenneth O. Stanley,et al.  Identifying Necessary Conditions for Open-Ended Evolution through the Artificial Life World of Chromaria , 2014, ALIFE.

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

[29]  Jean-Paul Delahaye,et al.  Two-dimensional Kolmogorov complexity and an empirical validation of the Coding theorem method by compressibility , 2012, PeerJ Comput. Sci..

[30]  Tomas Mikolov,et al.  A Roadmap Towards Machine Intelligence , 2015, CICLing.

[31]  Cristian S. Calude,et al.  Information and Complexity , 2017 .

[32]  Alexei A. Efros,et al.  Learning to Control Self-Assembling Morphologies: A Study of Generalization via Modularity , 2019, NeurIPS.

[33]  Brian J. LuValle.  The Effects of Boundary Conditions on Cellular Automata , 2019, Complex Syst..