Pascal's triangle of binomial coefficients C(n,k) rendered modulo a prime p, with 200 rows built via the recurrence C(n,k)=C(n−1,k−1)+C(n−1,k)(modp). For p=2 the nonzero cells trace out the Sierpinski triangle exactly; for higher primes Lucas' theorem C(n,k)≡i∏C(ni,ki)(modp),
where n=∑nipi and k=∑kipi are base-p expansions, forces a different self-similar gasket whose hollow sub-triangles have side pj. The simulation cycles through p∈{2,3,5,7,11} every six seconds, recoloring each residue class with a palette unique to the current prime so the change in fractal geometry between primes is unmistakable.