Symmetry in the Universe of Cellular Automata

  • Klaus MainzerEmail author
  • Leon Chua
Part of the SpringerBriefs in Complexity book series (BRIEFSCOMPLEXITY)


A cursory inspection of the discrete time evolutions of the 256 local rules reveals some similarity and partial symmetry among various evolved patterns. It reminds us of more-or-less random observations in the natural sciences that demand the unification of mathematical explanations with fundamental laws. The unifying theory of physics is based on the assumption of fundamental mathematical symmetries. According to this view, the variety and complexity of natural phenomena have evolved from just a few principles of symmetry. They are the “Holy Grail” of the Universe which is sought by prominent scientists and research groups all over the world. For the universe of cellular automata, we found the fundamental symmetries in the gallery of Boolean cubes. Thus, at least in the toy world of cellular automata, the importance of symmetry laws can easily be imagined and understood.


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Copyright information

© Klaus Mainzer 2012

Authors and Affiliations

  1. 1.Technische Unviversität München, Lehrstuhl für Philosophie und WissenschaftstheorieMunichGermany
  2. 2.EECS DepartmentUniversity of CaliforniaBerkeleyUSA

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