Publications 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. The story of geometry told by coins. The Canadian Numismatic Journal, 69(4):157--164, 2024. [ bib ]
[3] H. Fukś and J-M. Gómez Soto. Self-healing cellular automata, 2024. to be submitted. [ bib ]
[4] H. Fukś. Remembering Nino Boccara (1931--2018). J. of Cellular Automata, 17(5-6):461--477, 2023. [ bib | arXiv | http ]
[5] H. Fukś. Solvable cellular automata -- methods and applications. Springer, 2023. [ bib | DOI | http ]
[6] H. Fukś and S. A. Mudiyanselage. Deterministic cellular automata resembling diffusion. Int. J. Mod. Phys. C, 33(11):2250148, 2022. [ bib | DOI | arXiv ]
[7] 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 ]
[8] H. Fukś. Mathematics in the liturgical books of the Catholic Church: phases of the ecclesiastical moon. Antiquitates Mathematicae, 16:259--282, 2022. [ bib | DOI | http | .pdf ]
[9] H. Fukś. Rectification of the circle and magic squares -- works of Adam Kochański. Mówią Wieki, 732(1):24--27, 2021. [ bib | http ]
[10] H. Fukś. Mensurae universales magnitudinum ac temporum by Adam Adamandy Kochański -- Latin text with annotated English translation, 2021. [ bib | arXiv | http ]
[11] H. Fukś. Location prvilege of Władysław IV given to Wojciech Nowobilski - Latin text with Polish translation and explanatory note. Repository of Centre for Open Science, pages 1--6, 2021. art. no. 20378. [ bib | http | .pdf ]
[12] I. Moczydłowski. Białka Tatrzańska, osada z pierwszej połowy w XVII. na Podhalu. Repository of Centre for Open Science, art. no. 20311:1--14, 2021. Edited and annotated by H. Fukś. [ bib | http | .pdf ]
[13] 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 ]
[14] 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 ]
[15] 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 ]
[16] 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 ]
[17] John Clements, Babak Farzad, and Henryk Fukś. Dynamics of large-scale networks following a merger. In Tansel Özyer and Reda Alhajj, editors, Machine Learning Techniques for Online Social Networks, Lecture Notes in Social Networks, pages 173--193. Springer, Cham, 2018. [ bib | DOI | http ]
[18] H. Fukś. Explicit solution of the Cauchy problem for cellular automaton rule 172. J. of Cellular Automata, 12(6):423--444, 2017. [ bib | arXiv ]
[19] H. Fukś. Magic squares of subtraction of Adam Adamandy Kochański. In Maria Zack and Elaine Landry, editors, Research in History and Philosophy of Mathematics -- The CSHPM 2016 Annual Meeting in Calgary, AB, pages 81--95. Springer, 2017. [ bib | DOI | arXiv | http ]
[20] 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 ]
[21] K. Brudzynski, D. Miotto, L. Kim, C. Sjaarda, L. Maldonado-Alvarez, and H. Fukś. Active macromolecules of honey form colloidal particles essential for honey antibacterial activity and hydrogen peroxide production. Scientific Reports, 7:1--15, 2017. [ bib | DOI | .pdf ]
[22] 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 ]
[23] H. Fukś. Mathematical formulae on coins. part 2: from Pythagoras to the 20th century. The Canadian Numismatic Journal, 61(5):208--213, 2016. [ bib | arXiv ]
[24] H. Fukś. Mathematical formulae on coins. part 1: Einstein. The Canadian Numismatic Journal, 61(4):167--169, 2016. [ bib | arXiv ]
[25] J. Clements, B. Farzad, and H. Fukś. Dynamics of large scale networks following a merger. In Ravi Kumar, James Caverlee, and Hanghang Tong, editors, Proceedings of the 2016 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining, ASONAM 2016, pages 471--476, 2016. [ bib | DOI | http ]
[26] 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 ]
[27] 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 ]
[28] 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 ]
[29] H. Fukś. Three mathematical papers of Adam Adamandy Kochański -- annotated English translation. Antiquitates Mathematicae, 9:31--65, 2015. [ bib | DOI | http ]
[30] H. Fukś. Minimal entropy approximation for cellular automata. J. of Statistical Mechanics: Theory and Experiment, 4:P02009, April 2014. [ bib | DOI | arXiv ]
[31] H. Fukś, B. Farzad, and Y. Cao. A model of language inflection graphs. Int. J. Mod. Phys. C, 25(6):1450013, 2014. [ bib | DOI | arXiv ]
[32] 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 ]
[33] 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 ]
[34] H. Fukś. Construction of local structure maps for cellular automata. J. of Cellular Automata, 7:455--488, 2013. [ bib | arXiv ]
[35] H. Fukś. Adam Adamandy Kochański's approximations of π: reconstruction of the algorithm. Mathematical Intelligencer, 34:40--45, December 2012. [ bib | DOI | arXiv ]
[36] 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 ]
[37] 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 ]
[38] H. Fukś. Mysterious sequence in A. A. Kochański's Observationes Cyclometricae. In W. Wiesław, editor, Dzieje matematyki polskiej (History of Polish mathematics), pages 97--109. Instytut Matematyki Uniwersytetu Wroclawskiego, Wroclaw, 2012. [ bib | DOI | .pdf ]
[39] H. Fukś. Mathematics on coins, part I: The tale of two queens and two towering figures. The Canadian Numismatic Journal, 57(5):304--315, 2012. [ bib | arXiv ]
[40] 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 ]
[41] 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 ]
[42] H. Fukś. Probabilistic initial value problem for cellular automaton rule 172. DMTCS proc., AL:31--44, 2010. [ bib | DOI | arXiv ]
[43] 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 ]
[44] 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 ]
[45] 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 ]
[46] H. Fukś and M. Krzemiński. Topological structure of dictionary graphs. J. Phys. A: Math. Theor., 42:art. no. 375101, 2009. [ bib | DOI | .pdf ]
[47] H. Fukś. Inflection system of a language as a complex network. In Proceedings of 2009 IEEE Toronto International Conference -- Science and Technology for Humanity TIC-STH 2009, pages 491--496, 2009. [ bib | DOI | arXiv ]
[48] H. Fukś and M. Krzeminski. Core decomposition spectra of large graphs and their applications in modelling. In E. Wamkeue, editor, Proceedings of the 19th IASTED International Conference on Modelling and Simulation, pages art. no. 620--143. Acta Press, 2008. [ bib | .pdf ]
[49] 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 ]
[50] 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 ]
[51] H. Fukś. Dynamics of the cellular automaton rule 142. Complex Systems, 16:123--138, 2006. [ bib | arXiv | .pdf ]
[52] 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 ]
[53] H. Fukś, A. T. Lawniczak, and R. Duchesne. Effects of population mixing on the spread of SIR epidemics. Eur. Phys. J. B, 50:209--214, 2006. [ bib | DOI | arXiv ]
[54] A. T. Lawniczak, H. Fukś, and B. Di Stefano. Individually based SIR models, their motivation, and their spatio-temporal dynamics. Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal., 13B(suppl.):437--455, 2006. [ bib | http ]
[55] H. Fukś and C. Phipps. Toward a model of language acquisition threshold. In E. Wamkeue, editor, Proceedings of the 17th IASTED International Conference on Modellin g and Simulation, page 263. Acta Press, 2006. [ bib | .pdf ]
[56] H. Fukś. Percolation models. Wiadomości Naftowe i Gazowe, 7(99):14--16, 2006. [ bib | .pdf ]
[57] H. Fukś, R. Duchesne, and A. Lawniczak. Spatial correlations in SIR epidemic models. In Proceeding of 7th WSEAS International Conference on Applied Mathematics, Canun, Mexico, May 11-14 2005, pages 108--113, 2005. [ bib | arXiv ]
[58] H. Fukś. Probabilistic cellular automata with conserved quantities. Nonlinearity, 17:159--173, 2004. [ bib | DOI | arXiv ]
[59] 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 ]
[60] A. Gerisch, A.T. Lawniczak, R. A. Budiman, H. Fukś, and H. E. Ruda. Surface roughening in homoepitaxial growth: a lattice gas cellular automaton model. In M. A. Sloot, B. Chopard, and A. G. Hoekstra, editors, Cellular Automata, pages 286--295, Heidelberg, 2004. Springer. [ bib | DOI | arXiv ]
[61] H. Fukś. Sequences of preimages in elementary cellular automata. Complex systems, 14:29--43, 2003. [ bib | DOI | arXiv | .pdf ]
[62] 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 ]
[63] N. Boccara and H. Fukś. Number-conserving cellular automaton rules. Fundamenta Informaticae, 52:1--13, 2002. [ bib | arXiv | http ]
[64] H. Fukś. Non-deterministic density classification with diffusive probabilistic cellular automata. Phys. Rev. E, 66:066106, 2002. [ bib | DOI | arXiv ]
[65] H. Fukś, A. T. Lawniczak, and S. Volkov. Packet delay in models of data networks. ACM Transactions on Modelling and Simulations, 11:233--250, 2001. [ bib | DOI | arXiv ]
[66] H. Fukś and A. T. Lawniczak. Individual-based lattice model for the spatial spread of epidemics. Discrete Dynamics Dynamics in Nature and Society, 6:191--200, 2001. [ bib | DOI | arXiv ]
[67] H. Fukś and N. Boccara. Convergence to equilibrium in a class of interacting particle systems. Phys. Rev. E, 64:016117, 2001. [ bib | DOI | arXiv ]
[68] 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 ]
[69] 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 ]
[70] 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 ]
[71] B. Di Stefano, H. Fukś, and A. T. Lawniczak. Object-oriented implementation of CA/LGCA modelling applied to the spread of epidemics. In Proceedings of Canadian Conference on Electrical and Computer Engineering, Halifax, May 2000, pages 26--31, 2000. [ bib | DOI ]
[72] B. Di Stefano, H. Fukś, and A. T. Lawniczak. Application of fuzzy logic in CA/LGA models as a way of dealing with imprecise and vague data. In Proceedings of Canadian Conference on Electrical and Computer Engineering, Halifax, May 2000, pages 212--217, 2000. [ bib | DOI ]
[73] H. Fukś, A. T. Lawniczak, and B. Di Stefano. Epilab: software implementation of epidemic models based on lattice gas cellular automaton. Report FI-NP2000-003, The Fields Institute for Research in Mathematical Sciences, Toronto, 2000. [ bib ]
[74] H. Fukś and A. T. Lawniczak. Performance of data networks with random links. Mathematics and Computers in Simulation, 51:103--119, 1999. [ bib | DOI | arXiv ]
[75] H. Fukś. Exact results for deterministic cellular automata traffic models. Phys. Rev. E, 60:197--202, 1999. [ bib | DOI | arXiv ]
[76] H. Fukś and N. Boccara. Generalized deterministic traffic rules. Int. J. Mod. Phys. C, 9:1--12, 1998. [ bib | DOI | arXiv ]
[77] 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 ]
[78] 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 ]
[79] N. Boccara, H. Fukś, and S. Geurten. A new class of automata networks. Physica D, 103:145--154, 1997. [ bib | DOI | arXiv ]
[80] H. Fukś and N. Boccara. Cellular automata models for diffusion of innovations. Unpublished, 1997. [ bib | arXiv ]
[81] H. Fukś. Solution of the density classification problem with two cellular automata rules. Phys. Rev. E, 55:2081R--2084R, 1997. [ bib | DOI | arXiv ]
[82] 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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