TITLE: Behavior of Pascal's triangle in $n\mod m$ where $m>2$, any fractals?
QUESTION [7 upvotes]: If Sierpinski Triangles are found in 
Pascal's Triangle under modulo 2 what happens when we view Pascal's Triangle under modulo $m$ where $m>2$? Do fractals appear and if so for which numbers?
Related question, can we predict any behaviors if $m$ is prime?
I looked at $m=3$ with about fifty rows and saw a complicated pattern of upwards and downwards facing triangles be highlighted, but was unsure if the patterns were forming a fractal.

REPLY [7 votes]: Do fractals appear and if so for which numbers?

Here is what happens experimentally for $m=3..8$ for the first $100$ rows:
All of the pictures are for $C(n,k) \text{ mod } m=0$:


I see fractal strucutre for all the cases, however for primes it's much more simple than for composite numbers, which fits with Thomas' answer.

If we pick $C(n,k) \text{ mod } m=l,~l = 1,2,\dots,m-1$ we also obtain some kind of fractal structures, but different and usually more complicated than for $l=0$.

There is this excellent page which explains a lot about the topic, and with pictures (unlike most papers).
Namely, the pattern for compostie $m$ is a combination of patterns for their prime factors.