Simplicial sequences generalize the familiar "linear", "triangular", and "tetrahedral" number sequences. (A line segment is a 1-simplex, a triangle is a 2-simplex, a tetrahedron is a 3-simplex, and so on, so I'm calling these simplicial sequences.)
In general, the n-th d-simplicial number is the binomial coefficient C(n+d-1,d).
The pictures below graphically show the n-th element (modulo 512) of 512 simplicial sequences side by side. The white dots in a given frame have coordinates (d,C(n+d-1,d) mod 512), where d runs from 0 through to 511, and the value of n is displayed at the bottom of the diagram.
Also, if you are using a "modern browser" (i.e. not IE6,7,8), you can see an animation running through all values of n by following this link. The animation allows you to start and stop, and even save individual frames.
If you watch the animation, you'll see that binary visual patterns emerge, in ways that are threaded through the image and increase and decrease in strength. The images below for n=5 and n=256 indicate the extremes .. for n=5 the points look randomly distributed, for n=256 they are strongly patterned.
So my question is whether there are any explanations for the emergence and disappearance of visual binary patterns as we iterate through n.