Mandelbrot Explorer

Each fragment maps to a point on the complex plane. The complex square is written out in real arithmetic: the real part is a difference of squares, the imaginary part twice the product. The loop stops once the point has clearly escaped, tested against squared length so no square root is needed. Points that never escape are the set itself and are painted flat. For the rest, the raw count is an integer and shows up as hard bands, so the escape magnitude is folded back in through a double logarithm. That yields a continuous value across the boundary, and a cosine palette turns it into smooth colour.

Raise Zoom exponent one step at a time and watch detail continue past every scale until single precision floats run out and the image turns blocky. That limit is why deep zoom renderers use higher precision. Raise Iterations when zooming, since the budget that resolved the whole set reads as solid dark once you are inside a filament. Past roughly six the Center sliders are coarser than the view, so a fork wants pointer panning. Palette shift rotates colour without changing the maths.

Rarely a game effect directly, but the pattern is: a bounded iteration with an early exit, a squared distance test, and a continuous remap replacing an integer count. The same structure appears in raymarching loops and any per pixel search.