Both fractals here come from the same idea: pick a point, repeatedly feed it through z = z² + c, and watch whether the result stays bounded or shoots off to infinity. For the Mandelbrot set, c is the point itself and z always starts at zero; for a Julia set, z starts at the point and c is fixed for the whole image (the "seed" you can pick from the Mandelbrot set). A point is colored by how fast it escapes; points that never escape, no matter how long you wait, are the black interior. The catch is that "how fast" needs more and more iterations the deeper you zoom, because the escape behavior near the fractal boundary gets more delicate at every scale, which is also why this page pins every CPU core you have to a Web Worker instead of doing the math on one thread. Zooming has a floor, too: this renderer uses ordinary 64-bit floating point math, which only has about 15-17 significant decimal digits, so somewhere around 10¹³x magnification adjacent pixels start landing on the same floating-point number and the image degrades into blocky noise rather than finer detail. Going deeper than that needs arbitrary-precision or perturbation-based math, which is a possible future addition but out of scope here. The Autozoom button automates the descent: it zooms toward the center smoothly at your chosen speed, blitting a scaled copy of the last rendered frame every animation frame for instant feedback while only committing a fresh full-resolution render every so often, and it stops itself right at the precision floor described above.