Abstract
This paper shows the dynamics of Game of Life (Life) under delay-sensitive updating scheme where, during information sharing, neighbouring cells are associated with delay and probabilistic loss of information perturbation. Here, we explore the possibilities of continuous and abrupt change in phase during evolution of delay-sensitive Life. Next, we analyse the potential of micro-configurations (including oscillating, moving, stable micro-configurations) under delay-sensitive Life. Moreover, to understand the richness of Life, we observe the dynamics of extended Life rules and Life-like rules (both low and high density) under delay-sensitive environment.
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Notes
- 1.
Here, the term ‘structural’ indicates modification in the topological component interaction.
- 2.
a) blinker, (b) pulsar, (d) toad, (f) beacon, (g) largeblock.
- 3.
(c) glider, (e) spaceship.
- 4.
(h) beehive, (i) boat, (j) loaf, (k) ring, (l) ship, (m) tub.
References
Adachi, S., Lee, J., Peper, F., Umeo, H.: Kaleidoscope of life: a 24-neighbourhood outer-totalistic cellular automaton. Physica D 237(6), 800–817 (2008)
Adachi, S., Peper, F., Lee, J.: The game of life at finite temperature. Physica D 198(3), 182–196 (2004)
Berlekamp, E.R., Conway, J.H., Guy, R.K.: Winning Ways for Your Mathematical Plays, vol. 2. Academic Press, London (1984)
Bersini, H., Detours, V.: Asynchrony induces stability in cellular automata based models. In: Artificial Life IV: Proceedings of the Fourth International Workshop on the Synthesis and Simulation of Living Systems, pp. 382–387. The MIT Press (1994)
Blok, H.J., Bergersen, B.: Effect of boundary conditions on scaling in the “game of life". Phys. Rev. E 55, 6249–6252 (1997)
Blok, H.J., Bergersen, B.: Synchronous versus asynchronous updating in the “game of life". Phys. Rev. E 59, 3876–3879 (1999)
Das, S., Roy, S., Bhattacharjee, K.: The Mathematical Artist: A Tribute To John Horton Conway. Emergence, Complexity and Computation, Springer, Cham (2022). https://doi.org/10.1007/978-3-031-03986-7
de la Torre, A.C., Mártin, H.O.: A survey of cellular automata like the “game of life’’. Physica A Stat. Mech. Appl. 240(3), 560–570 (1997)
Eppstein, D.: Growth and Decay in Life-Like Cellular Automata, pp. 71–97. Springer, London (2010). https://doi.org/10.1007/978-1-84996-217-9_6
Fatès, N.: Does Life Resist Asynchrony?, pp. 257–274. Springer, London (2010). https://doi.org/10.1007/978-1-84996-217-9_14
Fatès, N., Morvan, M.: Perturbing the topology of the game of life increases its robustness to asynchrony. In: Sloot, P.M.A., Chopard, B., Hoekstra, A.G. (eds.) ACRI 2004. LNCS, vol. 3305, pp. 111–120. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-30479-1_12
Gardner, M.: Mathematical games: the fantastic combinations of John Conway’s new solitaire game “life”. Sci. Am. 223(4), 120–123 (1970)
Martínez, G.J., Adamatzky, A., Seck-Tuoh-Mora, J.C.: Some Notes About the Game of Life Cellular Automaton, pp. 93–104. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-03986-7_4
Monetti, R.A.: First-order irreversible phase transitions in a nonequilibrium system: mean-field analysis and simulation results. Phys. Rev. E 65, 016103 (2001)
Monetti, R.A., Albano, E.V.: Critical edge between frozen extinction and chaotic life. Phys. Rev. E 52, 5825–5831 (1995)
Neumann, J.V.: Theory of Self-Reproducing Automata. University of Illinois Press, Illinois (1966)
Peña, E., Sayama, H.: Life worth mentioning: complexity in life-like cellular automata. Artif. Life 27(2), 105–112 (2021)
Regnault, D., Schabanel, N., Thierry, É.: On the analysis of “Simple’’ 2D stochastic cellular automata. In: Martín-Vide, C., Otto, F., Fernau, H. (eds.) LATA 2008. LNCS, vol. 5196, pp. 452–463. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-88282-4_41
Roy, S.: A study on delay-sensitive cellular automata. Phys. A 515, 600–616 (2019)
Roy, S., Das, S., Mukherjee, A.: Elementary cellular automata along with delay sensitivity can model communal riot dynamics. Complex Syst. 31(3), 341–361 (2022)
Schulman, L.S., Seiden, P.E.: Statistical mechanics of a dynamical system based on Conway’s game of life. J. Stat. Phys. 19(3), 293–314 (1978)
Wolfram, S.: Two Different Directions: John Conway and Stephen Wolfram, pp. 21–71. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-03986-7_2
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Roy, S. (2024). Effect of Delay Sensitivity in Life and Extended Life. In: Dalui, M., Das, S., Formenti, E. (eds) Cellular Automata Technology. ASCAT 2024. Communications in Computer and Information Science, vol 2021. Springer, Cham. https://doi.org/10.1007/978-3-031-56943-2_2
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