An elementary monodimensional binary cellular automaton -184- with random white starting points -on the bottom line- [Un automate cellulaire binaire monodimensionnel élémentaire -184- avec des points aléatoires de départ blancs -sur la ligne du bas- ]

An elementary monodimensional binary cellular automaton -184- with random white starting points -on the bottom line- [Un automate cellulaire binaire monodimensionnel élémentaire -184- avec des points aléatoires de départ blancs -sur la ligne du bas-].




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 (Black) or 1 (White) 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 White. The time evolution of this set of cells is defined by means of rules.


This picture was computed using the following set of rules (B=Black, W=White): 
                    BBB = B
                    BBW = W
                    BWB = B
                    BWW = B
                    WBB = B
                    WBW = W
                    WWB = W
                    WWW = W
with, for example, "BWW = B" meaning: 
                    if ((CELL(x-1,t)==Black)&&(CELL(x,t)==White)&&(CELL(x+1,t)==White)) then CELL(x,t+1)=Black
This cellular automaton is called 184. As a matter of fact, when concatenating the right-hand sides of the preceding rules one obtains: 
                    --------   --------
                    BWBBBWWW = 01000111 = 10111000
and the binary number 10111000 equals the decimal number 184 (for 184=128+32+16+8). It can be displayed as the following cubes: 
                                    WWB=W---------------WWW=W                         W-------------------W
                                      /.                  /|                         /.                  /|
                                     / .                 / |                        / .                 / |
                                    /  .                /  |                       /  .                /  |
                                   /   .               /   |                      /   .               /   |
                                  /    .              /    |                     /    .              /    |
                               WBB=B---------------WBW=W   |                    B-------------------W     |
                                 |     .             |     |                    |     .             |     |
                                 |     .             |     |                    |     .             |     |
                                 |     .             |     |                    |     .             |     |
                                 |   BWB=B...........|...BWW=B                  |     B.............|.....B
                                 |    .              |    /                     |    .              |    /
                                 |   .               |   /                      |   .               |   /
                      ^          |  .                |  /                       |  .                |  /
                    Y |  Z       | .                 | /                        | .                 | /
                      | /        |.                  |/                         |.                  |/
                      |/       BBB=B---------------BBW=W                        B-------------------W
                      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 256 elementary monodimensional binary cellular automata with 1 white starting point (bottom left is the automata number 0 when top right is the number 255) and 256 elementary monodimensional binary cellular automata with 56% of white starting points (bottom left is the automata number 0 when top right is the number 255)).

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 03/21/2007 and last updated on 05/17/2026 17:58:34 -CEST-)



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