Jiří Kroc

The current frontiers in the description and simulation of advanced physical and biological phenomena observed within all scientific disciplines are pointing toward the importance of the development of robust mathematical descriptions that are error resilient. Complexity research is lacking deeper knowledge of the design methodology of processes that are capable to recreate the robustness, which is going to be studied on massive-parallel computations (MPCs) implemented by cellular automata (CA). A simple, two-state cellular automaton having an extremely simple updating rule, which was created by John H. Conway called the ’Game of Life’ (GoL) is applied to simulate and logic gate using emergents. This is followed by simulations of a robust, generalized GoL, which works with nine states instead of two, that is called R-GoL (open-source). extra states enable higher intercellular communication. The logic gate is simulated by the GoL. It is destroyed by injection of random faulty evaluations with even the smallest probability. The simulations of the R-GoL are initiated with random values. several types of emergent structures, which are robust to injection of random errors, are observed for different setups of the R-GoL rule. The GoL is not robust. The R-GoL is capable to create and maintain oscillating, emergent structures that are robust under constant injection of random, faulty evaluations with up to 1% of errors. The R-GoL express long-range synchronization, which is together with robustness facilitated by designed intercellular communication (pp.12-22).

Açar sözlər:Complex Systems, Cellular Automata, Emergence, Robustness, Artificial Life
DOI : 10.25045/jpis.v13.i2.02
  • Von Neumann, J. (1966). Theory of Self-Reproducing Automata. Illinois: University of Illinois Press (edited and completed by A.W. Burks).
  • Langton, C. (1984). Self-reproduction on a Cellular Automaton. Physica D, 10, 135–144.
  • Ilachinski, A. (2001). Cellular Automata: A Discrete Universe, Singapore: World Scientific Pub.
  • Kroc, J., Jiménez-Morales, F., Guisado, J.L., Lemos, M.C. & Tkáč, J. (2019). Building efficient computational cellular automata models of complex systems: backgrounds, applications, results, software, and pathologies. Advances in Complex Systems 22(05) 1950013
  • Kroc, J., Balihar, K., Matejovic, M. (2020). Complex Systems and Their Use in Medicine: Concepts, Methods and Bio-Medical Applications. preprint, ResearchGate, doi: 10.13140/RG.2.2.29919.30887
  • Kroc, J., Sloot, P.M., & Hoekstra, A. (2010). Simulating Complex Systems by Cellular Automata (Understanding Complex Systems). Berlin, Heidelberg: Springer. DOI: 10.1007/978-3-642-12203-3_1
  • Kroc, J., Sloot, P.M., & Hoekstra, A. (2010). Introduction to Modeling of Complex Systems Using Cellular Automata. In Kroc, J., Sloot, P.M., & Hoekstra, A. Simulating Complex Systems by Cellular Automata (Understanding Complex Systems). Berlin, Heidelberg: Springer. DOI:  10.1007/978-3-642-12203-3_1
  • Ilachinski, A. (2004). Artificial War: Multiagent-based Simulation of Combat, Singapore: World Scientific Pub.
  • Lorentz, E.N. (1963). Deterministic nonperiodic flow. Journal of the Atmospheric Sciences 20(2) 130-141. doi: 10.1175/1520-0469(1963)020CO;2
  • Boltzmann, L. (1896). Vorlesungen über Gastheorie, vol. I. Leipzig:J.A. Barth. (1st ed).
  • Boltzmann, L. (1898). Vorlesungen über Gastheorie, vol. II. Leipzig:J.A. Barth. (1st ed).
  • Jaynes, E.T. (1965). Gibbs vs Boltzmann entropies. American Journal of Physics, 33(5) 391–398.
  • Ben-Naim, A. (2015). Information, Entropy, Life and the Universe: What We Know and What We Do Not Know. Singapore: World Scientific Pub.
  • Shannon, C. E. (1948). A mathematical theory of communication. The Bell System Technical Journal, 27(3), 379-423.
  • Shannon, C. E., & Weaver, W. (1998). The Mathematical Theory of Communication. Urbana: University of Illinois Press.
  • Gardner, M., (1970). The Fantastic Combinations of John Horton Conway’s New Solitaire Game ‘Life’. Scientific American 223(4) 120–123. DOI 10.1038/scientificamerican1070-120
  • Wikipedia. (Dec 7, 2021). Conway's Game of Life. Retrieved from Wikipedia
  • Adamatzky, A. (2019). A brief history of liquid computers. Philosophical Transactions of the Royal Society B: Biological Sciences 374(1774) 20180372.
  • Wainwright, R.T. (1974). Life is Universal!. In, Proceedings of the 7th Conference on Winter Simulation - Vol 2 (pp. 449–459). Washington, DC. Doi 10.1145/800290.811303
  • Kroc, J. (2021). The simplest Python program simulating a cellular automaton model of a complex system: the 'Game of Life'. ResearchGate, open-source software. Retrieved from Source Code GoL
  • Sundnes, J. (2010). Introduction to Scientific Programming with Python. (Simula SpringerBriefs on Computing) Cham: Springer.
  • Langtangen, H.P. (2016). A Primer on Scientific Programming with Python. (Texts in Computational Science and Engineering 6) Berlin, Heidelberg: Springer, DOI: 1007/978-3-662-49887-3
  • Toffoli, T. (1984). Cellular automata as an alternative to (rather than an approximation of) differential equations in modeling physics. Physica D, 10(1–2), 117-127.
  • Vichniac, G. (1984). Simulating Physics with Cellular Automata. Physica D, 10, 96–115.
  • Silver, S. (2018). Life Lexicon. Retrieved from Life Lexicon
  • Carlini, N. (2021). A Simple CPU on the Game of Life – part 4. Retrieved from CPU made of GoL
  • Kroc, J. (2022). Python program simulating cellular automaton r-GoL that represents robust generalization of 'Game of Life'. ResearchGate, open-source software. Retrieved from Source Code of r-GoL'