The tridimensional John Conway's life game with random initial conditions -0.3% of occupied cells- and 20 iterations [*Le jeu de la vie tridimensionnel de John Conway avec des conditions initiales aléatoires -0.3% de cellules occupées- et 20 itérations*].

The bidimensional life game was initially defined by Conway. It uses an empty square mesh (all vertices are turned

[R1 = Birth] ((C(t).IS.The boundary conditions can be periodical or not.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)

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 3

[R1 = Birth] ((C(t).IS.The bidimensional and tridimensional processes can be extended one step further using two binary lists 'LD' and 'LA' ("Dead" -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)

[R1 = Birth] ((C(t).IS.In the bidimensional case the default 'LD' and 'LA' lists are: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)

LD="000100000" LA="110011110"

For this picture, the tridimensional mesh is 1024x1024x1024 and the parameters have the following arbitrary values:

LD="000111111110000000000000000" LA="110000000001111111111111110"

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[More information about the bidimensional John Conway's life game and the

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