Majority Adder Implementation by Competing Patterns in Life-Like Rule B2/S2345

We study Life-like cellular automaton rule B2/S2345. This automaton exhibits a chaotic behavior yet capable for purposeful computation. The automaton implements Boolean gates via patterns which compete for the space when propagate in channels. Values of Boolean variables are encoded into two types of patterns -- symmetric (FALSE) and asymmetric (TRUE).We construct basic logical gates and elementary arithmetical circuits by simulating logical signals using glider reactions taking place in the channels built of non-destructible still lifes. We design a binary adder of majority gates realised in rule B2/S2345.

[1]  Marvin Minsky,et al.  Computation : finite and infinite machines , 2016 .

[2]  Harold V. McIntosh.  Life's Still Lifes , 2010, Game of Life Cellular Automata.

[3]  John von Neumann,et al.  Theory Of Self Reproducing Automata , 1967 .

[4]  Master Gardener,et al.  Mathematical games: the fantastic combinations of john conway's new solitaire game "life , 1970 .

[5]  Stuart R. Hameroff,et al.  Ultimate computing - biomolecular consciousness and nanotechnology , 1987 .

[6]  Cristopher Moore,et al.  New constructions in cellular automata , 2003 .

[7]  Andrew Adamatzky,et al.  Game of Life Cellular Automata , 2010 .

[8]  Genaro Juárez Martínez,et al.  Localization Dynamics in a Binary Two-dimensional Cellular Automaton: the Diffusion Rule , 2009, J. Cell. Autom..

[9]  Jean-Philippe Rennard,et al.  Implementation of Logical Functions in the Game of Life , 2004, Collision-Based Computing.

[10]  Andrew Adamatzky,et al.  Collision-Based Computing , 2002, Springer London.

[11]  E. R. Banks.  INFORMATION PROCESSING AND TRANSMISSION IN CELLULAR AUTOMATA , 1971 .

[12]  Janko Gravner,et al.  Growth Phenomena in Cellular Automata , 2009, Encyclopedia of Complexity and Systems Science.

[13]  Tetsuya Asai,et al.  Reaction-diffusion computers , 2005 .

[14]  Wendy Goucher,et al.  The reality of trust , 2009 .

[15]  J. Schwartz,et al.  Theory of Self-Reproducing Automata , 1967 .

[16]  Juan Carlos Seck Tuoh Mora,et al.  Phenomenology of Reaction-diffusion Binary-State Cellular Automata , 2006, Int. J. Bifurc. Chaos.

[17]  E. F. Codd,et al.  Cellular automata , 1968 .

[18]  G. Jullien,et al.  Circuit design based on majority gates for applications with quantum-dot cellular automata , 2004, Conference Record of the Thirty-Eighth Asilomar Conference on Signals, Systems and Computers, 2004..

[19]  Hiroshi Umeo,et al.  Occurrence of Gliders in an Infinite Class of Life-Like Cellular Automata , 2008, ACRI.

[20]  Wolfgang Porod,et al.  Quantum-dot cellular automata : computing with coupled quantum dots , 1999 .

[21]  Andrew Adamatzky,et al.  On logical gates in precipitating medium: Cellular automaton model , 2008 .

[22]  Cristopher Moore,et al.  Life Without Death is P-complete , 1997, Complex Syst..

[23]  Claude Lattaud,et al.  Complexity Classes in the Two-dimensional Life Cellular Automata Subspace , 1997, Complex Syst..

[24]  S. Wolfram,et al.  Two-dimensional cellular automata , 1985 .

[25]  Paul W. Rendell,et al.  Turing Universality of the Game of Life , 2002, Collision-Based Computing.

[26]  M Mitchell,et al.  Life and evolution in computers. , 2001, History and philosophy of the life sciences.

[27]  P. A. Meehan,et al.  Analysis of Chaotic Instabilities in a Rotating Body with Internal Energy Dissipation , 2006, Int. J. Bifurc. Chaos.

[28]  Maurice Margenstern,et al.  Universality of Reversible Hexagonal Cellular Automata , 1999, RAIRO Theor. Informatics Appl..

[29]  T. Toffoli.  Non-Conventional Computers , 1998 .

[30]  Katsunobu Imai,et al.  A computation-universal two-dimensional 8-state triangular reversible cellular automaton , 2000, Theor. Comput. Sci..

[31]  A. Blokhuis.  Winning ways for your mathematical plays , 1984 .

[32]  David Eppstein.  Growth and Decay in Life-Like Cellular Automata , 2010, Game of Life Cellular Automata.

[33]  Andrew Adamatzky,et al.  Hot ice computer , 2009, 0908.4426.