Publications on cellular automata in chronological order

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[1] H. Fukś. Solving the initial value problem for cellular automata by pattern decomposition, 2024. to appear in Advances in Cellular Automata. [ bib ]
[2] H. Fukś and J-M. Gómez Soto. Self-healing cellular automata, 2024. to be submitted. [ bib ]
[3] H. Fukś. Solvable cellular automata -- methods and applications. Springer, 2023. [ bib | DOI | http ]
[4] H. Fukś and S. A. Mudiyanselage. Deterministic cellular automata resembling diffusion. Int. J. Mod. Phys. C, 33(11):2250148, 2022. [ bib | DOI | arXiv ]
[5] H. Fukś. Four state deterministic cellular automaton rule emulating random diffusion. In B. Chopard, editor, Cellular Automata, ACRI 2022, LNCS 13402, pages 142--152. Springer, 2022. [ bib | DOI | http ]
[6] H. Fukś and Y. Yin. Approximating dynamics of a number-conserving cellular automaton by a finite-dimensional dynamical system. Int. J. Mod. Phys. C, 31(12):2050172, 2020. [ bib | DOI | http ]
[7] H. Fukś and R. Procyk. Explorations of ternary cellular automata and ternary density classification problems. Acta Physica Polonica Supp., 12(1):75--89, 2019. [ bib | DOI | arXiv | http ]
[8] H. Fukś. Computing the density of ones in probabilistic cellular automata by direct recursion. In P. Y. Louis and F. R. Nardi, editors, Probabilistic Cellular Automata - Theory, Applications and Future Perspectives, Lecture Notes in Computer Science, pages 131--144. Springer, 2018. [ bib | DOI | arXiv ]
[9] Henryk Fukś and Francis Kwaku Combert. Evaluating the quality of local structure approximation using elementary rule 14. In Jan M. Baetens and Martin Kutrib, editors, Cellular Automata and Discrete Complex Systems - 24th IFIP WG 1.5 International Workshop, AUTOMATA 2018, Ghent, Belgium, June 20-22, 2018, Proceedings, volume 10875 of Lecture Notes in Computer Science, pages 43--56. Springer, 2018. [ bib | DOI | arXiv | http | .pdf ]
[10] H. Fukś. Explicit solution of the Cauchy problem for cellular automaton rule 172. J. of Cellular Automata, 12(6):423--444, 2017. [ bib | arXiv ]
[11] Henryk Fukś. Orbits of Bernoulli measures in cellular automata. In Robert A. Meyers, editor, Encyclopedia of Complexity and Systems Science, pages 1--19. Springer, Berlin, Heidelberg, 2017. [ bib | DOI | http ]
[12] H. Fukś and J. Midgley-Volpato. An example of a deterministic cellular automaton exhibiting linear-exponential convergence to the steady state. Acta Phys. Pol. B, 9(1):49--62, 2016. [ bib | arXiv | http ]
[13] H. Fukś and N. Fatès. Local structure approximation as a predictor of second-order phase transitions in asynchronous cellular automata. Natural Computing, 14:507--522, 2015. [ bib | DOI | arXiv ]
[14] H. Fukś. Solving two-dimensional density classification problem with two probabilistic cellular automata. Journal of Cellular Automata, 10(1--2):149--160, 2015. [ bib | arXiv ]
[15] H. Fukś and J. Midgley-Volpato. An example of degenerate hyperbolicity in cellular automaton with 3 states. In J. Kari, I. Törmä, and M. Szabados, editors, 21st International Workshop on Cellular Automata and Discrete Complex Systems, volume 24 of TUCS Lecture Notes, pages 47--55, Turku, Finland, 2015. [ bib | arXiv ]
[16] H. Fukś. Minimal entropy approximation for cellular automata. J. of Statistical Mechanics: Theory and Experiment, 4:P02009, April 2014. [ bib | DOI | arXiv ]
[17] H. Fukś and N. Fatès. Bifurcations of local structure maps as predictors of phase transitions in asynchronous cellular automata. In Lecture Notes in Computer Science, volume 8751, pages 556--560. Springer, 2014. [ bib | DOI | .pdf ]
[18] H. Fukś and J-M. Gómez Soto. Exponential convergence to equilibrium in cellular automata asymptotically emulating identity. Complex Systems, 23:1--26, 2014. [ bib | DOI | arXiv | .pdf ]
[19] H. Fukś. Construction of local structure maps for cellular automata. J. of Cellular Automata, 7:455--488, 2013. [ bib | arXiv ]
[20] H Fukś and A. Skelton. Orbits of Bernoulli measure in single-transition asynchronous cellular automata. Dis. Math. Theor. Comp. Science, AP:95--112, 2012. [ bib | DOI | http ]
[21] H. Fukś and A. Skelton. Classification of two-dimensional binary cellular automata with respect to surjectivity. In Proceedings of the 2012 International Conference on Scientific Computing: CSC-2012, pages 51--57. CSERA Press, 2012. [ bib | arXiv | .pdf ]
[22] H. Fukś and A. Skelton. Response curves and preimage sequences of two-dimensional cellular automata. In Proceedings of the 2011 International Conference on Scientific Computing: CSC-2011, pages 165--171. CSERA Press, 2011. [ bib | arXiv ]
[23] J-M. Gómez Soto and H. Fukś. Performance of the majority voting rule in solving the density classification problem in high dimension. J. Phys. A: Math. Theor., 44:art. no. 445101, 2011. [ bib | DOI | .pdf ]
[24] H. Fukś. Probabilistic initial value problem for cellular automaton rule 172. DMTCS proc., AL:31--44, 2010. [ bib | DOI | arXiv ]
[25] H. Fukś and A. Skelton. Response curves for cellular automata in one and two dimensions -- an example of rigorous calculations. International Journal of Natural Computing Research, 1:85--99, 2010. [ bib | DOI | arXiv ]
[26] H. Fukś and J. Haroutunian. Catalan numbers and power laws in cellular automaton rule 14. Journal of cellular automata, 4:99--110, 2009. [ bib | arXiv ]
[27] H. Fukś. Modeling, Simulation, and Optimization, chapter Cellular automata simulations - tools and techniques, pages 223--243. IN-TECH, Vienna, 2009. ISBN 978-953-307-056-8. [ bib | DOI | .pdf ]
[28] H. Fukś. Remarks on the critical behavior of second order additive invariants in elementary cellular automata. Fundamenta Informaticae, 78:329--341, 2007. [ bib | arXiv | http ]
[29] H. Fukś and K. Sullivan. Enumeration of number-conserving cellular automata rules with two inputs. Journal of Cellular Automata, 2:141--148, 2007. [ bib | arXiv | http ]
[30] H. Fukś. Dynamics of the cellular automaton rule 142. Complex Systems, 16:123--138, 2006. [ bib | arXiv | .pdf ]
[31] N. Boccara and H. Fukś. Motion representation of one-dimensional cellular automaton rules. Int. J. Mod. Phys. C, 17:1605--1611, 2006. [ bib | DOI | arXiv ]
[32] H. Fukś. Probabilistic cellular automata with conserved quantities. Nonlinearity, 17:159--173, 2004. [ bib | DOI | arXiv ]
[33] H. Fukś. Critical behaviour of number-conserving cellular automata with nonlinear fundamental diagrams. J. Stat. Mech.: Theor. Exp., 2004. art. no. P07005. [ bib | DOI | arXiv ]
[34] H. Fukś. Sequences of preimages in elementary cellular automata. Complex systems, 14:29--43, 2003. [ bib | DOI | arXiv | .pdf ]
[35] A. Gerisch, A. T. Lawniczak, R. A. Budiman, H. E. Ruda, and H. Fukś. Lattice gas cellular automaton modeling of surface roughening in homoepitaxial growth in nanowires. In Proceedings of Canadian Conference on Electrical and Computer Engineering, Montreal, May 2003, pages 1413--1416, 2003. [ bib | DOI | .pdf ]
[36] N. Boccara and H. Fukś. Number-conserving cellular automaton rules. Fundamenta Informaticae, 52:1--13, 2002. [ bib | arXiv | http ]
[37] H. Fukś. Non-deterministic density classification with diffusive probabilistic cellular automata. Phys. Rev. E, 66:066106, 2002. [ bib | DOI | arXiv ]
[38] H. Fukś and N. Boccara. Convergence to equilibrium in a class of interacting particle systems. Phys. Rev. E, 64:016117, 2001. [ bib | DOI | arXiv ]
[39] H. Fukś. Regularities in sequences of numbers of preimages in elementary cellular automata. Report FI-NP-2000-001, The Fields Institute for Research in Mathematical Sciences, Toronto, 2000. [ bib ]
[40] H. Fukś. A class of cellular automata equivalent to deterministic particle systems. In A. T. Lawniczak S. Feng and R. S. Varadhan, editors, Hydrodynamic Limits and Related Topics, Fields Institute Communications Series, Providence, RI, 2000. AMS. [ bib | DOI | arXiv ]
[41] N. Boccara and H. Fukś. Critical behavior of a cellular automaton highway traffic model. J. Phys. A: Math. Gen., 33:3407--3415, 2000. [ bib | DOI | arXiv ]
[42] H. Fukś. Exact results for deterministic cellular automata traffic models. Phys. Rev. E, 60:197--202, 1999. [ bib | DOI | arXiv ]
[43] H. Fukś and N. Boccara. Generalized deterministic traffic rules. Int. J. Mod. Phys. C, 9:1--12, 1998. [ bib | DOI | arXiv ]
[44] N. Boccara and H. Fukś. Modeling diffusion of innovations with probabilistic cellular automata. In M. Delorme and J. Mazoyer, editors, Cellular Automata: A Parallel Model, pages 263--277, Dordrecht, 1998. Kluwer Academic Publishers. [ bib | DOI | arXiv ]
[45] N. Boccara and H. Fukś. Cellular automaton rules conserving the number of active sites. J. Phys. A: Math. Gen., 31:6007--6018, 1998. [ bib | DOI | arXiv ]
[46] N. Boccara, H. Fukś, and S. Geurten. A new class of automata networks. Physica D, 103:145--154, 1997. [ bib | DOI | arXiv ]
[47] H. Fukś and N. Boccara. Cellular automata models for diffusion of innovations. Unpublished, 1997. [ bib | arXiv ]
[48] H. Fukś. Solution of the density classification problem with two cellular automata rules. Phys. Rev. E, 55:2081R--2084R, 1997. [ bib | DOI | arXiv ]
[49] N. Boccara, H. Fukś, and Q. Zeng. Car accidents and number of stopped cars due to road blockage on a one-lane highway. J. Phys. A: Math. Gen., 30:3329--3332, 1997. [ bib | DOI | arXiv ]

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