An elementary monodimensional binary cellular automaton -110- with 1 white starting point -bottom right- [*Un automate cellulaire binaire monodimensionnel élémentaire -110- avec 1 point de départ blanc -en bas et à droite-*].

An elementary monodimensional binary automaton is a monodimensional set of cells. At time 't', each cell (with coordinate 'x') has a value 'CELL(x,t)' that equals either 0 (

This picture was computed using the following set of rules:

BBB = W BBW = B BWB = B BWW = W WBB = B WBW = B WWB = B WWW = Wwith, for example, "BWW = W" meaning:

This cellular automaton is calledif((CELL(x-1,t)==Black)&&(CELL(x,t)==White)&&(CELL(x+1,t)==White))thenCELL(x,t+1)=White

-------- -------- WBBWBBBW = 10010001 = 01101110and the binary number 01101110 equals the decimal number 110 (for 110=64+32+8+4+2). It can be displayed as the following cubes:

WWB=B---------------WWW=W B-------------------W /. /| /. /| / . / | / . / | / . / | / . / | / . / | / . / | / . / | / . / | WBB=B---------------WBW=B | B-------------------B | | . | | | . | | | . | | | . | | | . | | | . | | | BWB=B...........|...BWW=W | B.............|.....W | . | / | . | / | . | / | . | / ^ | . | / | . | / Y | Z | . | / | . | / | / |. |/ |. |/ |/ BBB=W---------------BBW=B W-------------------B O----> Xthe 'X', 'Y' and 'Z' axes being respectively the 'Right', 'Left' and 'Current' axes.

By the way there are 256 different such elementary monodimensional binary cellular automata (see and ).

According to Matthew Cook, provided one can set up the right initial conditions (including, in an intricate way, both the data to be manipulated and the program instructions), this particular cellular automaton can support universal, Turing-complete computation.

The vertical axis is the time axis and the initial conditions are displayed on the bottom line.

[plus d'informations à propos des automates cellulaires monodimensionnels -en français/in french-]

[more information about monodimensional cellular automata -in english/en anglais-]

(CMAP28 WWW site: this page was created on 10/15/2002 and last updated on 04/26/2015 11:17:31 -CEST-)

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