Mathematical Visualisations

The majority are written in JavaScript and require a modern browser with support for SVG or canvas. Enjoy!

Animated Bézier Curves

Interactive animated parametric Bézier curves.

Animated Trigonometry

Animated projection of the unit circle, plotting graphs of sin, cos and tan simultaneously.

Apollonian Gasket

An interactive Apollonian Gasket, a fractal formed by recursively adding circles using simple rules.

Arnold’s Cat Map

Arnold’s Cat Map is a transformation that can be applied to an image.

Bifurcations in the Logistic Map

Repeated random sampling of the very simple logistic map equation for a range of reproduction/starvation rates produces a bifurcation diagram.

Sorting Visualisations

A visual comparison of merge sort and quicksort.

Complete Graphs

Complete graphs on n vertices, for n between 1 and 12.

DLA can be used to model systems such as lichen growth, the generation of polymers out of solutions, carbon deposits on the walls of a cylinder of a Diesel engine, path of electric discharge, and urban settlement.

Leibniz Spiral

A spiral visualisation of the Leibniz formula converging.

Morley Triangle

Trisect the angles of any triangle and the adjacent intersections will form an equilateral triangle.

Plants

Randomly generated plants.

Poincaré Disc

A tiling of the hyperbolic plane by ideal triangles.

Proof of Pythagoras’ Theorem

An interactive version of Sean B. Palmer’s proof.

From Random Polygon to Ellipse

Repeatedly applying simple rules to a random polygon will eventually form an ellipse.

Self-Organising Maps

A special type of unsupervised neural network used to automatically classify colours.

Tübingen

Slices of an n-dimensional regular lattice. Under construction, somewhat.

Fibonacci Numbers

Hilbert Curve

An approximation of the remarkable plane-filling curve.

Upside-Down Text

Maps each character to the equivalent Unicode character rotated by 180 degrees.