Sphere Lattices

Figure: A 4x4x4 lattice containing spheres of two sizes. Such lattices arise in crystallography, the evolution of cellular automata, and in many other places (like video games).

Just as molecules can be represented by collections of spheres, so also can crystal lattices. To avoid an endless proliferation of spheres, only a single unit cell would probably be drawn, although drawing a $3 \times 3 \times 3$ cluster would serve to illustrate the central environment better. Provided that the whole assemblage did not become too cluttered, that is.

Another interesting application of a sphere lattice is the representation of a three-dimensional cellular automaton; either the size or the color (or both) of the spheres would serve as an indicator of the state of the cell occupied by the sphere.

 
/* Fill a three dimensional lattice randomly */
/* p is probaility in mils                   */
/* n is lattice width (not number of points) */

void molla(s,p,n) double s[][7]; int p, n; {
int    i, j, k, ii;
double dx;
  dx=3.0/((double)(n-1));
for (i=0; i<n; i++) for (j=0; j<n; j++) for (k=0; k<n; k++) {
  ii=i+n*(j+n*k);
  s[ii][0]=-1.5+((double)i)*dx;
  s[ii][1]=-1.5+((double)j)*dx;
  s[ii][2]=-1.5+((double)k)*dx;
  s[ii][3]=(rand()%1024)<p?0.4*dx:0.166;
  s[ii][4]=(((double)(rand()%4096))/4096.0)*180.0;
  s[ii][5]=(((double)(rand()%4096))/4096.0)*180.0;
  s[ii][6]=(((double)(rand()%4096))/4096.0)*180.0;
  }
}