The tridimensional John Conway's life game with random initial conditions -2.0% of occupied cells- [Le jeu de la vie tridimensionnel de John Conway avec des conditions initiales aléatoires -2.0% 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 arbitrary values:
```                    LD="000010001110000011100010000"
LA="111111100011111110000111111"
```

See some related pictures (including this one):

(CMAP28 WWW site: this page was created on 03/12/2012 and last updated on 08/29/2024 20:55:22 -CEST-)

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