Now, explore Pascal's Triangle in terms of mod 3. This means that every entry is divided by 3, and replaced with the value of the remainder. So, the original 10 rows we were looking at before will now consist of either 0, 1, or 2.
Once we add different colors for our remainder values, the pattern is much easier to see. The 0 values have been left white, and red remains the color of all the 1 entries. Here, we have added blue to represent the cells with the value 2.
Now, let's expand our pattern to the 80th row! We can see that now the white space represents values that are multiples of 3. Notice again how the smaller triangle in the upper left corner is repeated at a larger and larger scale throughout the entire triangle. The blue triangle appears in each of the smaller triangle right in the middle between two red triangles. Notice how this pattern occurs regardless of the size of the triangles. What do you think the pattern would look like if we were to expand our entries even further?
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