64 elementary bidimensional binary cellular automata with 1 white starting central point [64 automates cellulaires binaires bidimensionnels élémentaires avec 1 point central de départ blanc].
An elementary bidimensional binary automaton is a bidimensional set of cells.
At time 't', each cell (with coordinate 'x' and 'y')
has a value 'CELL(x,y,t)' that equals either 0 (Black) or 1 (White)
and has eight neighbours.
The points outside the picture are assumed to be Black.
The time evolution of this set of cells is defined by means of rules.
For each 3x3 square, the Number of White points NW
is computed at time 't'.
This picture displays 8x8 (=64) such elementary bidimensional binary cellular automata.
They are computed using the 26 (=64) following arbitrary sets of rules:
if (NW(x,y,t)==0) then CELL(x,y,t+1)=B
if (NW(x,y,t)==1) then CELL(x,y,t+1)=W
if (NW(x,y,t)==2) then CELL(x,y,t+1)=a (B or W)
if (NW(x,y,t)==3) then CELL(x,y,t+1)=b (B or W)
if (NW(x,y,t)==4) then CELL(x,y,t+1)=c (B or W)
if (NW(x,y,t)==5) then CELL(x,y,t+1)=d (B or W)
if (NW(x,y,t)==6) then CELL(x,y,t+1)=e (B or W)
if (NW(x,y,t)==7) then CELL(x,y,t+1)=f (B or W)
if (NW(x,y,t)==8) then CELL(x,y,t+1)=B
if (NW(x,y,t)==9) then CELL(x,y,t+1)=W
The 8x8 small images display the 64 following cellular automata:
abcdef abcdef abcdef abcdef abcdef abcdef abcdef abcdef
WWWBBB BWWBBB WBWBBB BBWBBB WWBBBB BWBBBB WBBBBB BBBBBB
WWWWBB BWWWBB WBWWBB BBWWBB WWBWBB BWBWBB WBBWBB BBBWBB
WWWBWB BWWBWB WBWBWB BBWBWB WWBBWB BWBBWB WBBBWB BBBBWB
WWWWWB BWWWWB WBWWWB BBWWWB WWBWWB BWBWWB WBBWWB BBBWWB
WWWBBW BWWBBW WBWBBW BBWBBW WWBBBW BWBBBW WBBBBW BBBBBW
WWWWBW BWWWBW WBWWBW BBWWBW WWBWBW BWBWBW WBBWBW BBBWBW
WWWBWW BWWBWW WBWBWW BBWBWW WWBBWW BWBBWW WBBBWW BBBBWW
WWWWWW BWWWWW WBWWWW BBWWWW WWBWWW BWBWWW WBBWWW BBBWWW
For each automaton, the number of time steps equals 62.
(CMAP28 WWW site: this page was created on 01/21/2003 and last updated on 06/03/2024 14:23:56 -CEST-)
[See all related pictures (including this one) [Voir toutes les images associées (incluant celle-ci)]]
[Please visit the related NumberTheory picture gallery [Visitez la galerie d'images NumberTheory associée]]
[Go back to AVirtualMachineForExploringSpaceTimeAndBeyond [Retour à AVirtualMachineForExploringSpaceTimeAndBeyond]]
[The Y2K Bug [Le bug de l'an 2000]]
[Site Map, Help and Search [Plan du Site, Aide et Recherche]]
[Mail [Courrier]]
[About Pictures and Animations [A Propos des Images et des Animations]]
Copyright © Jean-François COLONNA, 2003-2024.
Copyright © France Telecom R&D and CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / École polytechnique, Institut Polytechnique de Paris, 2003-2024.