Life and Brain in the Universe of Cellular Automata

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


Historically, in science and philosophy people believed in a sharp difference between “dead” and “living” matter. Aristotle interpreted life as the power of self-organization (entelechy) driving the growth of plants and animals to their final form. A living system is able to reproduce itself and to move by itself, while a dead system can only be copied and moved from outside. Life was explained by teleology, i.e., by non-causal (“vital”) forces aiming at some goals in nature. In the eighteenth century Kant showed that self-organization of living organisms cannot be explained by a mechanical system of Newtonian physics. In a famous quotation he said that the Newton for explaining a blade of grass was still lacking. Nowadays, children put the same question: How is it possible that complex organisms such as plants, animals, and even humans emerge from the interactions of simple elements such as atoms, molecules, or cells? The concept of cellular automata was the first mathematical model to prove that self-reproduction and self-organization of complex patterns from simple rules are universal features of dynamical systems. Therefore, the belief in some preprogrammed intelligent design is unnecessary.


Cellular Automaton Cellular Automaton Synaptic Weight Cellular Neural Network Transcription Network 
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  1. U. Alon, Biological networks: the tinkerer as an engineer. Science 301, 1866–1867 (2003)ADSCrossRefGoogle Scholar
  2. U. Alon, An Introduction to Systems Biology Design Principles of Biological Circuits (Chapman & Hall/CRC, London, 2006)zbMATHGoogle Scholar
  3. L.O. Chua, Memristor–the missing circuit element. IEEE Trans. Circuit Theory 18, 507–519 (1971)CrossRefGoogle Scholar
  4. L.O. Chua, CNN: A Paradigm for Complexity (World Scientific, Singapore, 1998)zbMATHCrossRefGoogle Scholar
  5. L.O. Chua, Resistance switching memories are memristors. Appl. Phys. A 102(4), 765–783 (2011)ADSCrossRefGoogle Scholar
  6. L.O. Chua, T. Roska, Cellular Neural Networks and Visual Computing: Foundations and Applications (Cambridge University Press, Cambridge, 2002)CrossRefGoogle Scholar
  7. M. Creutz, Cellular automata and self-organized criticality. in Some New Directions in Science on Computers, ed. by G. Bhanot, S. Chen, P. Seiden. (Singapore, World Scientific, 1997), pp. 147–169Google Scholar
  8. M. Gardner, The fantastic combinations of John Conway’s new solitaire game of life. Sci. Am. 223, 120–123 (1970)CrossRefGoogle Scholar
  9. M. Gardner, Mathematical games: on cellular automata, self-reproduction, the Garden of Eden, and the game “Life”. Sci. Am. 224(2), 112–117 (1971)CrossRefGoogle Scholar
  10. G. Gerisch, B. Hess, Cyclic-AMP-controlled oscillations in suspended dictyostelium cells: their relation to morphogenetic cell interactions. Proc. Natl. Acad. Sci. 71, 2118 (1974)ADSCrossRefGoogle Scholar
  11. H. Haken, A. Mikhailov (eds.), Interdisciplinary Approaches to Nonlinear Complex Systems (Springer, New York, 1993)Google Scholar
  12. B. Hayes, The memristor. Am. Sci. 9(2), 106–110 (2011)CrossRefGoogle Scholar
  13. Y. Kayama, Complex networks derived from cellular automata (Cornell University arxiv.1009.4509v1, 2010)Google Scholar
  14. A. Kriete, R. Eils (eds.), Computational System Biology (Elsevier, Amsterdam, 2006)Google Scholar
  15. K. Mainzer, Cellular Neural Networks and visual computing. Int. J. Bifurc. Chaos 13(1), 1–6 (2003)ADSzbMATHCrossRefGoogle Scholar
  16. K. Mainzer, Thinking in Complexity. The Computational Dynamics of Matter, Mind, and Mankind, 5th edn. (Springer, Berlin, 2007)zbMATHGoogle Scholar
  17. K. Mainzer, Leben als Maschine? Von der Systembiologie zur Robotik und Künstlichen Intelligenz (Paderborn, Mentis, 2010)Google Scholar
  18. J. Mullins, Memristor minds: the future of artificial intelligence. New Scientist 7 (2009)Google Scholar
  19. D.B. Strukov, G.S. Snider, R. Duncan, D.R. Stewart, R.S. Williams, The missing memristor found. Nature 453, 80–83 (2008)ADSCrossRefGoogle Scholar
  20. R. Tetzlaff (ed.), Cellular Neural Networks and their Applications (World Scientific, Singapore, 2002)Google Scholar
  21. P. Topa, Network systems modelled by complex cellular automata paradigm. in Cellular Automata-Simplicity behind Complexity, ed. by A. Salcido. (InTech, 2011), pp. 259–274Google Scholar
  22. A.M. Turing, The chemical basis of morphogenesis. Philos. Trans. R. Soc. Lond. Ser. B Biol. Sci. 237(641), 37–72 (1952)ADSCrossRefGoogle Scholar

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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