When you take the remainder of dividing the
Fibonacci numbers
by a positive integer, you get a repeating pattern,

like 1, 1, 2 when dividing by 3. The length of the pattern is the
Pisano period for that divisor.
In this image, the

divisors increase in each row from 1 at the bottom to 24 at the top. From left to right are the
remainders of the

Fibonacci numbers (from 1 on the left) when divided by the divisor. The brighter the color,
the larger the number.

Yellowish squares on the left represent the first period for that divisor. Blueish disks
on the right show the repetition.

© 2013 Kerry Mitchell