I'm going to spend the rest of the evening thinking about this article

Furthermore, chaos reigned near the boundary. Two points might start very close together, bouncing side by side for a while, and then veer off to different roots. The winning root was as unpredictable as a game of roulette. Little things — tiny, imperceptible changes in the initial conditions — could make all the difference.

Hubbard’s work was an early foray into what’s now called “complex dynamics,” a vibrant blend of chaos theory, complex analysis and fractal geometry. In a way it brought geometry back to its roots. In 600 B.C. a manual written in Sanskrit for temple builders in India gave detailed geometric instructions for computing square roots, needed in the design of ritual altars. More than 2,500 years later, mathematicians were still searching for roots, but now the instructions were written in binary code.