A cinematic descent into the seahorse valley of the Mandelbrot set — 10,000 frames, 1.5 billion× magnification, up to 500,000 iterations per pixel.
Rendered offline in Python 3.11 using fractalshades, a library built on perturbation theory. At extreme zoom depths, standard 64-bit floating-point arithmetic loses all precision — perturbation theory sidesteps this by computing one high-precision reference orbit using arbitrary-precision arithmetic (mpmath), then approximating every other pixel as a small delta from that orbit in double precision.
10,000 frames were rendered individually to PNG at 854×480, with max iterations scaling adaptively from 5,000 at the surface to 500,000 at the deepest frames. The zoom follows a power-law ease-in curve so the early frames feel slow and contemplative before the dive accelerates. Camera rotation adds 540° of spiral over the full sequence. A Cython bug in fractalshades’s inner loop required a pure-Python fallback for the reference orbit computation at depth.