The amazing evolutionary dynamics of non-linear optical systems with feedback

Leonid Yaroslavsky*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Scopus citations


Optical systems with feedback are, generally, non-linear dynamic systems. As such, they exhibit evolutionary behavior. In the paper we present results of experimental investigation of evolutionary dynamics of several models of such systems. The models are modifications of the famous mathematical "Game of Life". The modifications are two-fold: "Game of Life" rules are made stochastic and mutual influence of cells is made spatially non-uniform. A number of new phenomena in the evolutionary dynamics of the models are revealed: - "Ordering of chaos". Formation, from seed patterns, of stable maze-like patterns with chaotic "dislocations" that resemble natural patterns, such as skin patterns of some animals and fishes, see shell, fingerprints, magnetic domain patterns and alike, which one can frequently find in the nature. These patterns and their fragments exhibit a remarkable capability of unlimited growth. - "Self-controlled growth" of chaotic "live" formations into "communities" bounded, depending on the model, by a square, hexagon or octagon, until they reach a certain critical size, after which the growth stops. - "Eternal life in a bounded space" of "communities" after reaching a certain size and shape. - "Coherent shrinkage" of "mature", after reaching a certain size, "communities" into one of stable or oscillating patterns preserving in this process isomorphism of their bounding shapes until the very end.

Original languageEnglish
Title of host publicationTribute to H. John Caulfield
StatePublished - 2013
EventTribute to H. John Caulfield - San Diego, CA, United States
Duration: 28 Aug 201328 Aug 2013

Publication series

NameProceedings of SPIE - The International Society for Optical Engineering
ISSN (Print)0277-786X
ISSN (Electronic)1996-756X


ConferenceTribute to H. John Caulfield
Country/TerritoryUnited States
CitySan Diego, CA


  • Deterministic chaos
  • Game of Life
  • Growth models
  • Non-linear dynamics
  • Pattern formation


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