Animated 3D generalization of the John Conway's
Game of Life.
3D Life was investigated by
In a M-dimentional Life a point has 3M - 1 neighbors,
i.e. 8 for 2D (M = 2) and 26 for 3D (M = 3).
Therefore in 3D we can get richer rules and structures.
You can play with rules and grid size to find interesting "life forms".
Will the life die whenever? :)
a new ball will appear if the number of neighbors (Sum) is equal or more than r1 and equal or less than r2.
a ball will die if the Sum is more than r3 or less than r4.
if ( (L[p]==0)&&(Sum[i][j][k]>=r1)&&(Sum[i][j][k]<=r2) ) L[p]=1; else if ( (L[p]!=0)&&((Sum[i][j][k]>r3)||(Sum[i][j][k]<r4)) ) L[p]=0;
You can set your own "initial structure" (e.g. "OOO") in a HTML file by
the applet tag
<param name=points value="3,-1 0 0,0 0 0,1 0 0">
where the first 3 is the number of points, then (i j k) coordinates of points go. The center of coordinate is in the center of the grid.
Michael Toftdal sent me several oscillators too.
Carter Bays found amazing 3D Gliders. See also Which "Life"-Like Systems Have Gliders? by David Eppstein.
Since I've got your messages with new suggestions, therefore I make a few examples too. See also Eric Weisstein's Treasure Trove of the Life CA, Stephen Silver's Life Page (but they don't like Java) and alife.co.uk. I was amazed when I found in Internet all these evident 2D grids and even 3,4D gliders. David Eppstein kindly sent me a reference about A CA run on Penrose Tiles by David Griffeath.
a *--*--* b .--*--. c *---* d *---. | | | | | | / \ / \ \ / \ *--o--* *--o--* *---o---* *---o .-- | | | | | | \ / \ / / \ / *--*--* .--*--. *---* *---.Honeycomb like lattice ("d" case) has non-equivalent nodes with 3 neighbors.
There are 14 different Bravais lattices in 3D. A node in the simple
cubic lattice has 26 neighbors (or only 6 nearest nodes). There are
8 and 12 neighbors in the body centered and face centered cubic
lattices correspondingly. A node in the close packed hexagonal lattice
has 12 neighbors too.
Diamond has a non-Bravais lattice with non-equivalent nodes and 4 neighbors.
And one can use quasi-crystall lattices (see Introduction to Quasicrystals). I think that every N-dimentional cube has a N-order rotation symmetry axis. Therefore we can make quasicrystals with any rotation symmetry axis by an appropriate projection of N-dimentional cubic lattice to 3D space. Where can I find these lattices for my students?
Don't think we need all these lattices. Really cellular automata seem me a little "artificial" yet. The Mandelbrot set is more "simple" and rich IMHO :)
6 neighbors Game
click here to read Belorussian translation