There are several similarities between the pattern generated from our mod 2 triangle and our mod 4 triangle. We would expect there to be some correlation because unlike the other mod's we have used, 4 is a multiple of 2. So numbers in Pascal's triangle that are divisible by 4 will also be divisible by 2. It is interesting to see, however that with mod 4 we will have remainders of 0, 1, 2, and 3. Notice that when a number is divided by four, and it's remainder is either 1 or 3, that number is odd. So all of the odd numbers from mod 2 (red) will either be 1's or 3's in mod 4 (red or yellow). Similarly, each of the even entries from mod 2 (white) will either be 0's or 2's in mod 4 (white or blue). Therefore our patterns look very similar.
Compare the first ten rows of Pascal's triangle below:
Now, compare the first 63 rows! See how the patterns of even and odd numbers in mod 2 is similar to the pattern of remainders in mod 4.
