Fibonacci Pinwheels: A Strange Source of Symmetry

(The Fibonacci sequence is a list of numbers that begins with a 1 followed by another 1, and continues by adding the previous two numbers together and tacking that sum on to the end of the list. The first ten numbers in the Fibonacci sequence are 1, 1, 2, 3, 5, 8, 13, 21, 34, and 55.
Modulo, or mod for short, means to divide a number by another number and then take the remainder. For example, “34 mod 10” is 4.
Phi is the name of the number that dividing 1 by it gives the same answer as subtracting 1 from it. It’s about 1.618.)

I was doodling in a grid-lined notebook one day when I came across the idea to map Fibonacci sequence number pairs to coordinates in a 10×10 grid. I outlined such a grid in my notebook, labeled the axes 0-9 because I was going to graph it modulo 10, and started filling in boxes.