Natural Computing

, Volume 12, Issue 4, pp 573–588 | Cite as

An experimental study of noise and asynchrony in elementary cellular automata with sampling compensation

Article

Abstract

This article focuses on the set of 32 legal elementary cellular automata (ECA). We perform an exhaustive study of the systems’ response under: (i) α-asynchronous dynamics, from full asynchronism to perfect synchrony, (ii) κ-scaling, which extends α-asynchrony to compensate for less cell activity, and (iii) ϕ-noise scheme, a perturbation that affects the local transition function and causes a cell to probabilistically miscalculate the new state when it is updated. We propose a new classification in three classes under asynchronous conditions: α-invariant, α-robust, and α-dependent. We classify the 32 legal ECA according to the degree of behavioural modification, and we show that our classifying scheme provides results coherent with the density-based classification. We also show that κ-scaling provides results comparable to synchronous systems, both quantitatively and qualitatively. Subsequently, we analyse the effects of including different levels of noise in synchronous systems. We identify different responses to noise, including systems that are robust to asynchrony and susceptible to noise. To conclude, we investigate the behavioural changes caused by simultaneous asynchrony and noise in models tolerant to both perturbations. We describe a number of effects caused by the interplay of noise and asynchrony, thus further reinforcing that both aspects are pertinent for future studies.

Keywords

Asynchronism Classification Elementary cellular automata Local transition function Noise 

Supplementary material

11047_2013_9387_MOESM1_ESM.zip (329 kb)
ZIP (330 KB)

References

  1. Bandini S, Bonomi A, Vizzari G (2012) An analysis of different types and effects of asynchronicity in cellular automata update schemes. Nat Comput 11(2):277–287MathSciNetCrossRefGoogle Scholar
  2. Berry H (2003) Nonequilibrium phase transition in a self-activated biological network. Phys Rev E 67(3):031,907CrossRefGoogle Scholar
  3. Bersini H, Detours V (1994) Asynchrony induces stability in cellular automata based models. In: 4th international conference on simulation & synthesis of living systems (ALIFE IV). MIT Press, Cambridge, pp 382–387Google Scholar
  4. Blok HJ, Bergersen B (1999) Synchronous versus asynchronous updating in the game of life. Phys Rev E 59(4):3876CrossRefGoogle Scholar
  5. Bouré O, Fatès N, Chevrier V (2012) Probing robustness of cellular automata through variations of asynchronous updating. Nat Comput. doi: 10.1007/s11047-012-9340-y
  6. Braga G, Cattaneo G, Flocchini P, Vogliotti C (1995) Pattern growth in elementary cellular automata. Theor Comput Sci 145(1–2):1–26CrossRefMATHGoogle Scholar
  7. Cattaneo G, Finelli M, Margara G (2000) Investigating topological chaos by elementary cellular automata dynamics. Theor Comput Sci 244(1–2):219–241MathSciNetCrossRefMATHGoogle Scholar
  8. Chevrier V, Fatès N (2008) Multi-agent systems as discrete dynamical systems: influences and reactions as a modelling principle. Tech. rep., INRIA-LORIA. http://hal.inria.fr/inria-00345954
  9. Cornforth D, Green D, Newth D (2005) Ordered asynchronous processes in multi-agent systems. Physica D 204(1):70–82MathSciNetCrossRefGoogle Scholar
  10. Correia L (2006) Self-organisation: a case for embodiment. In: Gershenson C, Lenaerts T (eds) Evolution of complexity workshop, held as part of the 10th international conference on simulation and synthesis of living systems (ALIFE X), pp 111–116Google Scholar
  11. Correia L (2006) Self-organised systems: fundamental properties. Revista de Ciências da Computação 1(1):9–26Google Scholar
  12. Correia L, Wehrle T (2006) Cellular automata under the influence of noise. eprint arXiv:nlin/0604071 Xiv:nlin/0604071Google Scholar
  13. Dennunzio A, Formenti E, Manzoni L (2012) Computing issues of asynchronous CA. Fundam Inf 120(2):165–180MathSciNetMATHGoogle Scholar
  14. Dennunzio A, Formenti E, Provillard J (2012) Non-uniform cellular automata: classes, dynamics, and decidability. Inf Comput 215:32–46MathSciNetCrossRefMATHGoogle Scholar
  15. Dennunzio A, Formenti E, Manzoni L, Mauri G (2013) m-asynchronous cellular automata: from fairness to quasi-fairness. Nat Comput. http://hdl.handle.net/10281/43525
  16. Fatès N (2003) Experimental study of elementary cellular automata dynamics using the density parameter. Discret Math Theor Comput Sci AB:155–166Google Scholar
  17. Fatès N (2006) Directed percolation phenomena in asynchronous elementary cellular automata. In: Yacoubi SE, Chopard B, Bandini S (eds) 7th international conference on cellular automata for research and industry (ACRI’06). Springer, Heidelberg, pp 667–675Google Scholar
  18. Fatès N (2009) Asynchrony induces second order phase transitions in elementary cellular automata. J Cell Autom 4(1):21–38MathSciNetMATHGoogle Scholar
  19. Fatès N, Morvan M (2005) An experimental study of robustness to asynchronism for elementary cellular automata. Complex Syst 16(1):1–27Google Scholar
  20. Fatès N, Regnault D, Schabanel N, Thierry E (2006) Asynchronous behavior of double-quiescent elementary cellular automata. In: Correa JR, Hevia A, Kiwi M (eds) LATIN 2006: theoretical informatics, Lecture notes in computer science, vol 3887. Springer, Heidelberg, pp 455–466Google Scholar
  21. Fuks H, Skelton A (2011) Orbits of the Bernoulli measure in single-transition asynchronous cellular automata. In: 17th international workshop on cellular automata and discrete complex systems (Automata 2011). Discrete Mathematics and Theoretical Computer Science, pp 95–112. http://www.dmtcs.org/dmtcs-ojs/index.php/proceedings/article/view/dmAP0107
  22. Gács P (2001) Reliable cellular automata with self-organization. J Stat Phys 103(1–2):45–267CrossRefMATHGoogle Scholar
  23. Gács P, Reif J (1988) A simple three-dimensional real-time reliable cellular array. J Comput Syst Sci 36(2):125–147CrossRefMATHGoogle Scholar
  24. Glass L (2001) Synchronization and rhythmic processes in physiology. Nature 410(6825):277–284CrossRefGoogle Scholar
  25. Grilo C, Correia L (2011) Effects of asynchronism on evolutionary games. J Theor Biol 269(1):109–122MathSciNetCrossRefGoogle Scholar
  26. Gunji Y (1990) Pigment color patterns of molluscs as an autonomous process generated by asynchronous automata. Biosystems 23(4):317–334CrossRefGoogle Scholar
  27. Hamming R (1950) Error detecting and error correcting codes. Bell Syst Tech J 29(2):147–160MathSciNetCrossRefGoogle Scholar
  28. Ingerson T, Buvel R (1984) Structure in asynchronous cellular automata. Physica D 10(1–2):59–68MathSciNetCrossRefGoogle Scholar
  29. Inghe O (1989) Genet and ramet survivorship under different mortality regimes a cellular automata model. J Theor Biol 138(2):257–270MathSciNetCrossRefGoogle Scholar
  30. Kanada Y (1997) The effects of randomness in asynchronous 1d cellular automata. Techical report, Tsukuba Research CenterGoogle Scholar
  31. Mallet D, De Pillis L (2006) A cellular automata model of tumor–immune system interactions. J Theor Biol 239(3):334–350MathSciNetCrossRefGoogle Scholar
  32. Manzoni L (2012) Asynchronous cellular automata and dynamical properties. Nat Comput 11(2):269–276MathSciNetCrossRefGoogle Scholar
  33. Ódor G, Szolnoki A (1996) Directed-percolation conjecture for cellular automata. Phys Rev E 53(3):2231–2238CrossRefGoogle Scholar
  34. Ódor G, Boccara N, Szabó G (1993) Phase-transition study of a one-dimensional probabilistic site-exchange cellular automaton. Phys Rev E 48(4):3168–3171CrossRefGoogle Scholar
  35. Regnault D (2006) Abrupt behaviour changes in cellular automata under asynchronous dynamics. In: 2nd European conference on complex systems (ECCS 2006), pp 116–121. http://www.cabdyn.ox.ac.uk/complexity_PDFs/ECCS06/Conference_Proceedings/PDF/p116.pdf
  36. Regnault D (2013) Proof of a phase transition in probabilistic cellular automata. In: Bal MP, Carton O (eds) Developments in language theory, Lecture notes in computer science, vol 7907. Springer, Heidelberg, pp 433–444Google Scholar
  37. Roca CP, Cuesta JA, Sánchez A (2009) Effect of spatial structure on the evolution of cooperation. Phys Rev E 80(4):046,106CrossRefGoogle Scholar
  38. Roca CP, Cuesta JA, Sánchez A (2009) Evolutionary game theory: temporal and spatial effects beyond replicator dynamics. Phys Life Rev 6(4):208–249CrossRefGoogle Scholar
  39. Ruxton GD, Saravia LA (1998) The need for biological realism in the updating of cellular automata models. Ecol Model 107(2–3):105–112CrossRefGoogle Scholar
  40. Schönfisch B, de Roos A (1999) Synchronous and asynchronous updating in cellular automata. Biosystems 51(3):123–143CrossRefGoogle Scholar
  41. Silva F, Correia L (2011) Noise and intermediate asynchronism in cellular automata with sampling compensation. In: 15th Portuguese conference on artificial intelligence (EPIA’11), pp 209–222Google Scholar
  42. Silva F, Correia L (2012) A study of stochastic noise and asynchronism in elementary cellular automata. In: Sirakoulis GC, Bandini S (eds) 10th international conference on cellular automata for research and industry (ACRI 2012), Lecture notes in computer science, vol 7495. Springer, Heidelberg, pp 679–688Google Scholar
  43. Smith H (1935) Synchronous flashing of fireflies. Science 82(2120):151–151CrossRefGoogle Scholar
  44. Strogatz SH, Stewart I (1993) Coupled oscillators and biological synchronization. Sci Am 269(6):102–109CrossRefGoogle Scholar
  45. Toom A (1980) Multicomponent random systems, Advances in probability. In: Stable and attractive trajectories in multicomponent systems, vol 6. Marcel Dekker, New York Google Scholar
  46. Weifeng F, Lizhong Y, Weicheng F (2003) Simulation of bi-direction pedestrian movement using a cellular automata model. Physica A 321(3):633–640CrossRefMATHGoogle Scholar
  47. Wolfram S (1983) Statistical mechanics of cellular automata. Rev Mod Phys 55(3):601–644MathSciNetCrossRefMATHGoogle Scholar
  48. Wolfram S (1985) Twenty problems in the theory of cellular automata. Phys Scr T9:170–183MathSciNetCrossRefGoogle Scholar
  49. Wolfram S (2002) A new kind of science. Wolfram Media, ChampaignMATHGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Instituto de TelecomunicaçõesLisbonPortugal
  2. 2.LabMAg, Faculdade de Ciências da Universidade de LisboaLisbonPortugal

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