Gilbreath's conjecture produces an triangular matrix of witch the most elements are either $0$, or $2$. When using different colors for those two elements, very interesting triangular structured trees in all kind of variations can be observed, this image is generated by simply coloring all zero elemts in red and all two elements in green, all other colors on the top are simply demonstrating how long it takes until the deeper gaps between the primes get zeroed/twoed out by the absolute values of the ongoing differences.
My question is, what additional rules could be applied to the generated Gilbreath's conjecture matrix to generate a tetrahedronic tensor from this, with the same kind of tetrahedronical tree structures in all variations?