Pascal's triangle mod p

Divide every number in Pascal's triangle by a prime p and keep only the remainder. When the number of rows is a power of p, the triangle falls apart into p(p + 1)/2 smaller triangles shaped like the whole, though coloured by residue each one has its remainders multiplied through by a constant; the upside-down gaps between them hold nothing but multiples of p, and for p = 2 this is Sierpiński's triangle. Colour by carries and the colour tells how many times p divides the number, which is how many times you carry when adding k and n − k in base p. Click an entry and the corner writes its row and place in base p, working out its remainder digit by digit.