The good old times tables lead a very exciting secret life involving the infamous Mandelbrot set, the ubiquitous cardioid and a myriad of hidden beautiful patterns. Time for the Mathologer to go on a serious fact-finding mission.
The discovery of the stunning patterns that I discuss in this video is due to the mathematician Simon Plouffe.
Check out this article http://tinyurl.com/o2hbtsa and his website http://plouffe.fr for other stunning visualisations using modular arithmetic.