Math might just be a formal game we play, but fractals seem to point toward something higher, something hauntingly Platonic.

This video shows a part of the Mandelbrot set, a famously simple equation which tirelessly unfolds into an infinitely elaborate landscape.

As you remember from algebra, the real numbers can be represented on a number line. Complex numbers, which have a real part and an imaginary part, can be represented on a number plane, with the real part on the x axis and the imaginary part on the y axis. “Real” and “imaginary” are misnomers; both flavors of number are equally real (or equally imaginary, if you’re a skeptic), so complex numbers should just be thought of as 2D entities that have all the properties required to enable counting, plus some more general directional properties which play an important role in algebra.

The Mandelbrot set is calculated by repeatedly squaring every number in the complex plane, then adding it to itself, squaring it again, adding it to its original self again, and so on, in an iterative process. When you do this, small enough numbers will stay finite, large numbers will grow quickly toward infinity, and medium-sized numbers will grow at different rates relative to each other. The white patterns in this video are areas where the complex numbers are growing slowly relative to their neighbors.

It took my laptop a few hours to calculate this. Each frame has 4 million complex numbers, with a few hundred iterations at each point, for a few billion calculations per frame. And it’s a 60 fps video, so in total it’s a few dozen trillion repetitions of that simple formula.

The pattern’s structural richness arises in part from the huge number of calculations involved, but in essence this is just the flowering of a tiny seed which has been given ample computational nutrition. And that seed’s beautiful potential, which has waited implicitly and invisibly in logical abstraction long before anyone drew it out, hints that math may be more than just a formulaic story we tell; the Mandelbrot set, at least, seems to have roots which extend beyond time. What else is in that soil?