🔍 2D Fractal Explorer — Mandelbrot & Julia

Both compute the same escape-time algorithm, but this one runs entirely in JavaScript on a flat 2D canvas using putImageData, while the other renders through a GLSL fragment shader inside a Three.js scene. This version is slower per pixel but easier to inspect and modify, and it recomputes the exact same z = z² + c iteration by hand rather than on the GPU.

To stay responsive, the renderer samples a coarser grid of pixels while you're actively panning or zooming, then fills in the full-resolution pass a fraction of a second after you stop. This keeps the interaction smooth even though every pixel is genuinely iterated in JavaScript rather than drawn from a pre-rendered texture.

With that box ticked and Julia mode selected, dragging anywhere on the canvas maps your cursor position directly onto the complex plane and uses that point as the Julia constant c, live-updating the sliders and the fractal as you move. It is a direct, exploratory way to browse the whole family of Julia sets instead of typing numbers.

Yes — every pixel undergoes the real iteration z = z² + c with the standard escape radius test, computed with standard double-precision numbers. The smooth colouring is purely a display technique; it does not change which points are treated as escaping.

Double-precision JavaScript numbers carry roughly 15-17 significant decimal digits. Past a few million times zoom, the difference between neighbouring pixels' coordinates becomes smaller than that precision can represent, so the escape-time calculation starts producing rounding artefacts instead of genuine structure.