# mathr / blog / #

## Crisis (deep zoom)

Deep zoom is a subgenre of fractal video art. Shapes in the Mandelbrot set (and other fractals) stack up in nested period-doubling crises as you pass by mini-sets and the embedded Julia sets between them.

Mandelbrot set deep zooms are computationally expensive, requiring lots of high precision numerical calculations. Computational cost has a corresponding ecological cost. The climate is the real crisis.

This is not a Mandelbrot set deep zoom, but it might resemble one at first glance with its nested period-doubling crises. But instead it is designed to have a similar appearance with much cheaper equations.

Rendering of v1 (duration one hour) at 1920x1080p60@50Mbps took a little over four hours wall-clock time. Two-pass video encoding to 960x540p60@4Mbps took a little over half an hour wall-clock time. I estimate around 1kWh of electricity was used.

Summary of the key parts of the algorithm:

for (l = L; l >= 0; --l)
t = -log2(1 - t)
n += floor(t)
t -= floor(t)
t = (1 - exp2(-t)) * 2
// store n and t for level l

Drone soundtrack based on the same code used for the graphics.