Where it shows up
The same escape-time bookkeeping appears wherever a simple map is iterated near a boundary. Newton's method for finding roots paints its own fractal basins, colouring which starting guess lands on which solution. Complex dynamics uses the Mandelbrot set as an atlas: each point records whether the matching Julia set is one connected piece or scattered dust. The self-similar roughness also echoes coastlines, turbulence and river networks, all cases where structure repeats across scales rather than settling onto a single length.
The knobs
- Set: choose Julia, where drifts and the shape morphs, or Mandelbrot, where the plane holds still and the palette cycles.
- Max iterations: the escape budget. Raising it sharpens the fine tendrils along the boundary, at the cost of more computation per frame.
- Zoom: tightens the view around the centre, magnifying detail that keeps unfolding however close you look.
- Colour cycle: sets how densely the palette repeats across the escape gradient, packing more or fewer bands into the same picture.