Advances in the Evolution of Complex Cellular Automata

  • Michal BidloEmail author
Part of the Studies in Computational Intelligence book series (SCI, volume 792)


In this study we present some advanced experiments dealing with the evolutionary design of multi-state uniform cellular automata. The generic square calculation problem in one-dimensional automata will be treated as one of the case studies. An analysis of the evolutionary experiments will be proposed and properties of the resulting cellular automata will be discussed. It will be demonstrated that various approaches to the square calculations in cellular automata exist, some of which substantially overcome the known solution. The second case study deals with a non-trivial pattern development problem in two-dimensional automata. Some of the results will be presented which indicate that an exact behaviour can be automatically designed even for cellular automata working with more than ten cell states. A discussion for both case studies is included and potential areas of further research are highlighted.


Evolutionary algorithm Cellular automaton Transition function Conditional rule Square calculation Pattern development 



This work was supported by The Ministry of Education, Youth and Sports of the Czech Republic from the National Programme of Sustainability (NPU II), project IT4Innovations excellence in science – LQ1602, and from the Large Infrastructures for Research, Experimental Development and Innovations project “IT4Innovations National Supercomputing Center – LM2015070”.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Faculty of Information Technology, IT4Innovations Centre of ExcellenceBrno University of TechnologyBrnoCzech Republic

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