3D fractal worlds
These are ray marched: for every pixel, a ray steps out from a virtual camera and uses a distance estimate of the fractal to find its surface, then lights it like polished metal.
Mandelbulb
The best-known 3D cousin of the Mandelbrot set. Slide the Power control and the bulb melts from a smooth blob into coral, cauliflower and alien seed pods.
Mandelbox
Folding and stretching space over and over builds impossible architecture: towers, vaults and corridors that repeat at every scale.
Menger Sponge
A cube with its middle removed, then the middle of every smaller cube removed, forever. Infinite surface area with zero volume, and you can fly through it.
Kaleidoscopic IFS
Mirror folds repeated many times grow an alien cathedral of arches and spires. Drag to pan, scroll to zoom, and change the Fold to rebuild it.
Quaternion Julia
A Julia set computed in four dimensions and sliced into three, rendered as liquid chrome that slowly flows into new shapes.
Dive
An endless descent down a metallic Mandelbulb tunnel. The walls keep revealing finer self-similar detail, so the fall never ends.
Classic fractals, reimagined
The 2D sets repeat a simple formula at every point of the plane and colour each point by how quickly it escapes. Here they get smooth colouring and simulated metal lighting.
The Weave
The front page: a metallic blend that morphs between the Mandelbrot set and its Julia sets. Zoom into the detail and save any frame as a 4K or 8K wallpaper.
Living Julia Set
A single Julia set whose seed drifts continuously, so its spirals and islands are always forming, joining and breaking apart in liquid metal.
Phoenix
A fractal that remembers its previous step, which gives it feathery wings and spirals. Snap it to the upright Phoenix pose and save it.
Nova Basins
Built from Newton's method for finding roots. The three-fold basins spin and bloom, with fine filigree wherever the method can't decide.
Kleinian Circles
Circles packed inside circles inside circles. A gallery of inversions in the spirit of Indra's Pearls, packing endlessly deeper.
Cosmic Nebula
Layered noise rendered as glowing gas, a bright core and scattered stars. A calm, slowly drifting piece to leave running.
Math in motion
Not all of these are fractals, but they all grow beautiful structure from simple rules.
Mandelbrot & Julia Pair
Drag a point on the Mandelbrot set and watch its matching Julia set change beside it. The clearest way to see how the two are connected.
Strange Attractors
Lorenz, Aizawa, Thomas, Clifford and more, drawn as glowing trails. Chaotic systems that never repeat yet always keep the same shape.
Fractal Flames
Millions of points thrown through random warping functions build soft, glowing flames. Every press of New flame grows a different one.
Reaction-Diffusion
Two simulated chemicals react and spread, growing the spots, stripes and mazes Alan Turing proposed for animal markings. Paint into it with the mouse.
Chladni Figures
Sand on a vibrating metal plate gathers along the lines that stay still. Sweep the frequency and watch the figure snap between patterns.
Complex Function Art
Every point of the plane is coloured by where a complex function sends it, so zeros and poles bloom into colour wheels.
