The Mandelbrot set is every complex number c for which z → z² + c, starting fromz = 0, never escapes to infinity. Each pixel is a value of c. The GPU runs that loop for every pixel in parallel in a fragment shader, and colours the pixel by how fast it escaped (using a "smooth" iteration count so you don't get bands). Black pixels never escaped.

Julia mode fixes c and varies the starting z instead. Move the mouse to changec (each position corresponds to a point near the Mandelbrot set), and click to lock it.

It isn't truly infinite here: GPUs use 32-bit floats with about 7 significant digits, so somewhere around a 10⁵–10⁶× zoom neighbouring pixels map to the same number and the picture turns blocky. Going deeper needs emulated double precision or perturbation theory, which is a rabbit hole for another day.