The Minimum Number of Iterations Required to Replicate Binary Images using Discrete One-dimensional Dynamical Systems and a Retrocausal Updation Rule
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10.5120/ijca2021921183 |
Sugata Mitra. The Minimum Number of Iterations Required to Replicate Binary Images using Discrete One-dimensional Dynamical Systems and a Retrocausal Updation Rule. International Journal of Computer Applications 174(26):6-12, March 2021. BibTeX
@article{10.5120/ijca2021921183, author = {Sugata Mitra}, title = {The Minimum Number of Iterations Required to Replicate Binary Images using Discrete One-dimensional Dynamical Systems and a Retrocausal Updation Rule}, journal = {International Journal of Computer Applications}, issue_date = {March 2021}, volume = {174}, number = {26}, month = {Mar}, year = {2021}, issn = {0975-8887}, pages = {6-12}, numpages = {7}, url = {http://www.ijcaonline.org/archives/volume174/number26/31836-2021921183}, doi = {10.5120/ijca2021921183}, publisher = {Foundation of Computer Science (FCS), NY, USA}, address = {New York, USA} }
Abstract
Agents affected by their own future states in a one-dimensional discrete dynamical system (1-DDS) can replicate two-dimensional images. A novel and practical set of two rules have been developed in this paper to calculate the number of iterations required for exact replication. It is argued that retrocausal updation used by 1-DDS can replicate any n-dimensional digital object. It is shown that the way iterations reach a final image are different for randomly generated images and non-random images. This paper suggests a simple method for replicating and detecting non-randomness in images.
References
- Wolfram, S. (1983). “Statistical Mechanics of Cellular Automata,” Reviews of Modern Physics, 55 601–644. http://lattice.ifsc.usp.br/~lattice/oldlattice/artigo-wolfram-cellular-autom.pdf
- Willson, S. J. “Cellular Automata Can Generate Fractals,” Discrete Applied Mathematics, 8(1), 1984 pp. 91–99.doi:10.1016/0166-218X(84)90082-9.
- Willson, S. J. “Computing Fractal Dimensions for Additive Cellular Automata,” Physica D: Nonlinear Phenomena, 24(1–3), 1987 pp. 190–206. doi:10.1016/0167-2789(87)90074-1.
- Willson, S. J. “Growth Rates and Fractional Dimensions in Cellular Automata,” Physica D: Nonlinear Phenomena, 10(1–2), 1984 pp. 69–74. doi:10.1016/0167-2789(84)90250-1.
- Culik II, K. and Dube, S. “Fractal and Recurrent Behavior of Cellular Automata,” Complex Systems, 3(3), 1989 pp. 253–267. complex-systems.com/pdf/03-3-3.pdf.
- Fredkin, E. “An Informational Process Based on Reversible Universal Cellular Automata,” Physica D: Nonlinear Phenomena, 45(1–3), 1990 pp. 254–270. doi:10.1016/0167-2789(90)90186-S.
- Mitra, S. and Kumar, S. “Fractal Replication in Time-Manipulated One-Dimensional Cellular Automata,” Complex Systems, 16(3), 2006 pp. 191–197. complex-systems.com/pdf/16-3-1.pdf.
- Gravner, J. and Griffeath, D. “The One-Dimensional Exactly 1 Cellular Automaton: Replication, Periodicity, and Chaos from Finite Seeds,” Journal of Statistical Physics, 142(1), 2011 pp. 168–200. doi:10.1007/s10955-010-0103-9.
- Inabathini, S. & L. J. Replication of a Binary Image on a One-Dimensional Cellular Automaton with Linear Rules. Complex Systems. 2018;27(4):415–430. Available from: 10.25088/ComplexSystems.27.4.415
- An introduction to discrete dynamical systems, Internet: “Math Insight” https://mathinsight.org/discrete_dynamical_system_introduction
- Bonabeau, Eric (2002). Agent-based modeling: Methods and techniques for simulating human systems, PNAS vol. 99 suppl. 3, pp7280–7287. https://www.pnas.org/content/99/suppl_3/7280 .
- Shiffman, D. (2012). Chapter 7, The Nature of Code – Simulating Natural Systems with Code. https://www.amazon.com/Nature-Code-Simulating-Natural-Processing/dp/0985930802
- Rouhaud, J. (2000). Cellular automata and consumer behaviour, European Journal of Economic and Social Systems 14 N° 1 37-52. https://ejess.edpsciences.org/articles/ejess/pdf/2000/01/rouhaud.pdf?access=ok
- Duhamel, P. and Kieffer, M. Joint Source-Channel Decoding (2010), Academic Press, https://doi.org/10.1016/C2009-0-19065-7
- Mitra, Sugata.(2002) ‘Meaning in Binary Strings’, Introduction to Multimedia Systems, Academic Press, pp. 151. Also downloadable from https://7551850c-18fa-45d6-98bc-8e2829cc3850.filesusr.com/ugd/369ee5_d5ddac04b3e14a37939ed8b1f8f521f3.pdf
- Corona Virus Data (2020), from ourworldindata.org https://ourworldindata.org/coronavirus-source-data
Keywords
Image replication, retrocausality, toroidal spacetime, discrete dynamical systems, cellular automata, agents