![](image.jpg)
The tridimensional John Conway's life game with random initial conditions -23% of occupied cells- [Le jeu de la vie tridimensionnel de John Conway avec des conditions initiales aléatoires -23% de cellules occupées-].
The bidimensional life game
was initially defined by Conway. It uses an empty
square mesh (all vertices are turned off).
At time t=0 some vertices are occupied (they are turned on): this is the initial
state. To go from the time t to the time t+1, it suffices
to count for each vertex -or "Cell"- C(x,y) the number N of its
neighbours (it is less than or equal to 32-1=8) and then to possibly change the state of
M according to the following bidimensional automata
rules:
[R1 = Birth] ((C(t).IS.off).AND.(N == 3)) ==> C(t+1) on
[R2 = Death] ((C(t).IS.on).AND.((N < 2).OR.(N > 3))) ==> C(t+1) off
[R3] other cases ==> C(t+1)=C(t)
The boundary conditions can be periodical or not.
This process can be extended in a tridimensional space. The number N
of neighbours of the vertex -or "Cell"- C(x,y,z) is computed
(it is less than or equal to 33-1=26) and
the preceding rules can be extended as follows:
[R1 = Birth] ((C(t).IS.off).AND.((N >= NB1).AND.(N <= NB2))) ==> C(t+1) on
[R2 = Death] ((C(t).IS.on).AND.((N < ND1).OR.(N > ND2))) ==> C(t+1) off
[R3] other cases ==> C(t+1)=C(t)
The bidimensional and tridimensional processes can be extended one step further using two binary lists
'LD' and 'LA' ("Dead" -off- and "Alive" -on- respectively):
[R1 = Birth] ((C(t).IS.off).AND.(LD[N] == 1)) ==> C(t+1)=on
[R2 = Death] ((C(t).IS.on).AND.(LA[N] == 1)) ==> C(t+1)=off
[R3] other cases ==> C(t+1)=C(t)
In the bidimensional case the default 'LD' and 'LA' lists are:
LD="000100000"
LA="110011110"
("1" means "to change the state" and "0" means "the state is unchanged").
For this picture, the parameters have the following values:
NB1=10
NB2=14
ND1=8
ND2=16
See a related picture with less cells:
See some related pictures (including this one):
[More information about the bidimensional John Conway's life game and the bidimensional extended life game]
(CMAP28 WWW site: this page was created on 02/25/2012 and last updated on 08/29/2024 20:52:00 -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, 2012-2024.
Copyright © CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / École polytechnique, Institut Polytechnique de Paris, 2012-2024.