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 (**B**lack) or 1 (**W**hite)
and has two neighbours (one at its left 'CELL(x-1,t)' and one at its right 'CELL(x+1,t)').
The points outside the picture (at left and at right) are assumed to be **W**hite.
The time evolution of this set of cells is defined by means of rules.

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 = W

with, for example, "BWW = W" meaning:
**if** ((CELL(x-1,t)==**B**lack)&&(CELL(x,t)==**W**hite)&&(CELL(x+1,t)==**W**hite)) **then** CELL(x,t+1)=**W**hite

This cellular automaton is called **110**. As a matter of fact,
when concatenating the right-hand sides of the preceding rules one obtains:
-------- --------
WBBWBBBW = 10010001 = 01101110

and 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---->
X

the '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 01/28/2014
15:33:08 -CET-)

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Copyright (c) Jean-François Colonna, 2002-2014.

Copyright (c) France Telecom R&D and CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / Ecole Polytechnique, 2002-2014.