This demo graphically shows the n-th element (modulo 512) of 512 simplicial sequences side by side. 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.
In general, the n-th d-simplicial number is C(n+d-1,d).
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.
You can increment n one value at a time by using the Step button.
Use the Run button to let n advance automatically.
Use the Reset button to reset the sequences.
Save a picture in your browser with the Save Image button. Then download the picture if you want.