Render the Mandelbrot set live, colored by iteration count from the PIGMENTUM palette.
The Mandelbrot set is the most famous object in mathematics that you can actually see. For each point on the complex plane, a simple equation is iterated; some points stay bounded forever (the black heart of the set) while others fly off to infinity. How quickly a point escapes — its iteration count — is what produces the intricate, infinitely detailed boundary, and it is exactly what we use to choose a color.
The canvas is rendered live in your browser. Each pixel is iterated up to the limit you set; the escape count is mapped onto a hue sweep so that bands of equal escape time share a color, producing the classic rainbow contours around the set. Points that never escape are drawn black. Raising the iteration limit reveals finer structure at the boundary.
Below the canvas, the iteration bands are sampled and each is matched to an exact named PIGMENTUM color, so a piece of pure mathematics becomes a concrete, named palette you can reuse. The rendering is intentionally modest in size to stay fast on phones; the math is identical at any resolution.
Mathematics enthusiasts, generative and creative coders, and designers hunting for an algorithmic palette with a story.