The Mandelbrot set, in three dimensions — no mesh, no model, computed per pixel
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Math: the classical Mandelbrot set iterates z → z2 + c over the complex numbers. The Mandelbulb does the same in three dimensions with the White–Nylander “power 8”: write the point in spherical coordinates (r, θ, φ), take r → r8, θ → 8θ, φ → 8φ, add c, repeat; a point belongs to the set when the iteration does not escape. Dev: raymarching with Hart’s distance estimator, DE = ½·log(r)·r/r′: each pixel fires a ray and steps forward by the distance the estimator guarantees is free, until it grazes the surface; the normal is the gradient of the same estimator, the shading is diffuse plus cheap occlusion (how many steps it took) plus a Fresnel rim; the colour runs from the theme’s primary to its accent by orbit trap (the smallest radius the orbit reached). A few kilobytes of shader your graphics card compiles in milliseconds — nothing to download, no library. Honest scope: nothing here is a result of ours; it is a classical object (Daniel White and Paul Nylander, 2009) drawn live so that you can see a shape that is a computation rather than a picture of one. It has no size in metres: a Mandelbulb is a mathematical object, not a thing in space.
Each pixel iterates z → z8 + c in spherical coordinates and marches a ray to where the set’s surface is — there is no mesh and no model, the shape is the iteration, computed live on your graphics card. It used to sit at the bottom of the front page, on the Redheffer lattice, as the last of the live pieces; it belongs here, with the rest of the things that are computed rather than shown. The shader is checked by tests/mandelbulb.check.mjs, which re-implements the iteration on the CPU and requires the served shader to use exactly it (power 8, spherical, + c). It stops when it is off screen or the tab is in the background, and draws one still frame for visitors who asked for less motion. Needs WebGL2; without it the card stays empty and says nothing false.