Fractals on FoundingFuture

Anatomy of the Mandelbrot set

Sun, 30 Aug 2026 12:54:33 +0200

The pictures that carry the name Mandelbrot show a black bulb with spirals and curls along its edge. They are coloured in bands, and magnifying the edge reveals more detail without end. Those pictures are portraits of a set of complex numbers. One short calculation, repeated, decides which numbers belong. This page defines the set, works that calculation, and names the shapes the picture turns out to hold.

Palette morphing between waypoints

Tue, 08 Sep 2026 00:20:00 +0200

Each waypoint of a movie carries its own palette and its own colour cycle density, and the renderer interpolates both across the move between them.

A zoom movie is a list of waypoints and the camera moves between them. Each waypoint carries the two settings that decide colour. One is the palette the frame is drawn in. The other is how many colour cycles the picture spans. The renderer interpolates both across every move, on the same eased parameter that drives the zoom. A frame at a stopped waypoint is drawn exactly as that waypoint defines it. Every frame between two waypoints is part of the way from one setting to the other.

Mandelbrot zoom movies

Mon, 07 Sep 2026 23:44:11 +0200

Tours of the boundary, rendered frame by frame from a list of waypoints.

A movie is a list of waypoints and the camera moves between them. A waypoint fixes a centre, a view height, an iteration ceiling and the colouring. Every frame is a full escape-time render, so the cost grows with the length of the movie and with the depth it reaches. Each entry below carries the video, the points it dives to and what it took.