IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v151y2021ics0960077921006263.html
   My bibliography  Save this article

Lerch distribution based on maximum nonsymmetric entropy principle: Application to Conway’s game of life cellular automaton

Author

Listed:
  • Contreras-Reyes, Javier E.

Abstract

Conway’s Game of Life (GoL) is a biologically inspired computational model which can approach the behavior of complex natural phenomena such as the evolution of ecological communities and populations. The GoL frequency distribution of events on log-log scale has been proved to satisfy the power-law scaling. In this work, GoL is connected to the entropy concept through the maximum nonsymmetric entropy (MaxNSEnt) principle. In particular, the nonsymmetric entropy is maximized to lead to a general Zipf’s law under the special auxiliary information parameters based on Hurwitz–Lerch Zeta function. The Lerch distribution is then generated, where the Zipf, Zipf–Mandelbrot, Good and Zeta distributions are analyzed as particular cases. In addition, the Zeta distribution is linked to the famous golden number. For GoL simulations, the Good distribution presented the best performance in log-log linear regression models for individual cell population, whose exponents were far from the golden number. This result suggests that individual cell population decays slower than a hypothetical slope equal to a (fast decaying) negative golden number.

Suggested Citation

  • Contreras-Reyes, Javier E., 2021. "Lerch distribution based on maximum nonsymmetric entropy principle: Application to Conway’s game of life cellular automaton," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    • Handle: RePEc:eee:chsofr:v:151:y:2021:i:c:s0960077921006263
    DOI: 10.1016/j.chaos.2021.111272
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077921006263
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2021.111272?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Kun Wu & Qiong Nan & Tianqi Wu, 2020. "Philosophical Analysis of the Meaning and Nature of Entropy and Negative Entropy Theories," Complexity, Hindawi, vol. 2020, pages 1-11, August.
    2. Contreras-Reyes, Javier E., 2015. "Rényi entropy and complexity measure for skew-gaussian distributions and related families," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 433(C), pages 84-91.
    3. Wei, Jinling & Zhou, Haiyan & Meng, Jun & Zhang, Fan & Chen, Yunmo & Zhou, Su, 2016. "The SOC in cells’ living expectations of Conway’s Game of Life and its extended version," Chaos, Solitons & Fractals, Elsevier, vol. 89(C), pages 348-352.
    4. Contreras-Reyes, Javier E., 2021. "Chaotic systems with asymmetric heavy-tailed noise: Application to 3D attractors," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    5. Liu, Cheng-shi, 2009. "Nonsymmetric entropy and maximum nonsymmetric entropy principle," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2469-2474.
    6. Stakhov, Alexey, 2006. "Fundamentals of a new kind of mathematics based on the Golden Section," Chaos, Solitons & Fractals, Elsevier, vol. 27(5), pages 1124-1146.
    7. Zornig, Peter & Altmann, Gabriel, 1995. "Unified representation of Zipf distributions," Computational Statistics & Data Analysis, Elsevier, vol. 19(4), pages 461-473, April.
    8. Cerruti, Umberto & Dutto, Simone & Murru, Nadir, 2020. "A symbiosis between cellular automata and genetic algorithms," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Zhao, Tong & Li, Zhen & Deng, Yong, 2023. "Information fractal dimension of Random Permutation Set," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    2. Yu, Zihan & Deng, Yong, 2022. "Derive power law distribution with maximum Deng entropy," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
    3. Kharazmi, Omid & Contreras-Reyes, Javier E., 2023. "Deng–Fisher information measure and its extensions: Application to Conway’s Game of Life," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    4. Zhao, Tong & Li, Zhen & Deng, Yong, 2024. "Linearity in Deng entropy," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    5. Refah Alotaibi & Faten S. Alamri & Ehab M. Almetwally & Min Wang & Hoda Rezk, 2022. "Classical and Bayesian Inference of a Progressive-Stress Model for the Nadarajah–Haghighi Distribution with Type II Progressive Censoring and Different Loss Functions," Mathematics, MDPI, vol. 10(9), pages 1-19, May.
    6. Pedro Carpena & Ana V. Coronado, 2022. "On the Autocorrelation Function of 1/ f Noises," Mathematics, MDPI, vol. 10(9), pages 1-12, April.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Contreras-Reyes, Javier E., 2022. "Rényi entropy and divergence for VARFIMA processes based on characteristic and impulse response functions," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    2. Kwame Boamah‐Addo & Tomasz J. Kozubowski & Anna K. Panorska, 2023. "A discrete truncated Zipf distribution," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 77(2), pages 156-187, May.
    3. Estrada, Ernesto, 2007. "Graphs (networks) with golden spectral ratio," Chaos, Solitons & Fractals, Elsevier, vol. 33(4), pages 1168-1182.
    4. Büyükkılıç, F. & Demirhan, D., 2009. "Cumulative growth with fibonacci approach, golden section and physics," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 24-32.
    5. Izsak, F., 2006. "Maximum likelihood estimation for constrained parameters of multinomial distributions--Application to Zipf-Mandelbrot models," Computational Statistics & Data Analysis, Elsevier, vol. 51(3), pages 1575-1583, December.
    6. Stakhov, Alexey, 2006. "The golden section, secrets of the Egyptian civilization and harmony mathematics," Chaos, Solitons & Fractals, Elsevier, vol. 30(2), pages 490-505.
    7. Falcón, Sergio & Plaza, Ángel, 2007. "The k-Fibonacci sequence and the Pascal 2-triangle," Chaos, Solitons & Fractals, Elsevier, vol. 33(1), pages 38-49.
    8. Young, D.S., 2013. "Approximate tolerance limits for Zipf–Mandelbrot distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(7), pages 1702-1711.
    9. Juan Carlos Seck-Tuoh-Mora & Joselito Medina-Marin & Norberto Hernández-Romero & Genaro J. Martínez, 2023. "Mean-Field Analysis with Random Perturbations to Detect Gliders in Cellular Automata," Mathematics, MDPI, vol. 11(20), pages 1-13, October.
    10. Contreras-Reyes, Javier E. & Kharazmi, Omid, 2023. "Belief Fisher–Shannon information plane: Properties, extensions, and applications to time series analysis," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    11. Javier E. Contreras-Reyes & Mohsen Maleki & Daniel Devia Cortés, 2019. "Skew-Reflected-Gompertz Information Quantifiers with Application to Sea Surface Temperature Records," Mathematics, MDPI, vol. 7(5), pages 1-14, May.
    12. Christian H. Weiß, 2013. "Integer-valued autoregressive models for counts showing underdispersion," Journal of Applied Statistics, Taylor & Francis Journals, vol. 40(9), pages 1931-1948, September.
    13. Valero, Jordi & Pérez-Casany, Marta & Duarte-López, Ariel, 2022. "The Zipf-Polylog distribution: Modeling human interactions through social networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 603(C).
    14. El Naschie, M.S., 2006. "An elementary proof for the nine missing particles of the standard model," Chaos, Solitons & Fractals, Elsevier, vol. 28(5), pages 1136-1138.
    15. El Naschie, M.S., 2006. "Is Einstein’s general field equation more fundamental than quantum field theory and particle physics?," Chaos, Solitons & Fractals, Elsevier, vol. 30(3), pages 525-531.
    16. Lucio Palazzo & Riccardo Ievoli, 2022. "A Semiparametric Approach to Test for the Presence of INAR: Simulations and Empirical Applications," Mathematics, MDPI, vol. 10(14), pages 1-18, July.
    17. Cerruti, Umberto & Dutto, Simone & Murru, Nadir, 2020. "A symbiosis between cellular automata and genetic algorithms," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    18. Zörnig, Peter, 2010. "Statistical simulation and the distribution of distances between identical elements in a random sequence," Computational Statistics & Data Analysis, Elsevier, vol. 54(10), pages 2317-2327, October.
    19. Sarabia, José María & Gómez-Déniz, Emilio & Sarabia, María & Prieto, Faustino, 2010. "A general method for generating parametric Lorenz and Leimkuhler curves," Journal of Informetrics, Elsevier, vol. 4(4), pages 524-539.
    20. Rajaram, R. & Castellani, B., 2016. "An entropy based measure for comparing distributions of complexity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 453(C), pages 35-43.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:151:y:2021:i:c:s0960077921006263. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.