Pattern - Cyclic Behavior

Modulo creates cycles. The values of $n \bmod 5$ repeat in the pattern $0, 1, 2, 3, 4, 0, 1, 2, 3, 4, ...$ as $n$ increases.

This is perfect for circular arrays or rotating through options. If you have an array of length $n$ and want to access index $i$ where $i$ might exceed $n$, use $i \bmod n$.

For example, days of the week cycle every $7$ days. If today is day $3$ (Wednesday) and you want to know the day $100$ days from now, compute $(3 + 100) \bmod 7 = 5$ (Friday).