Pretty Math Pictures

This gallery showcases some of our best fractal & mathematical pictures. Start here! We have Mandelbrot & Julia Sets, Lorenz… read more The Very Best Fractal & Mathematical Pictures

This is a simple harmonograph simulator to generate random-ish harmonographs. It asks for the number of pendulums, and exits if… read more Multi-pendulum Harmonograph simulator using numpy and matplotlib

This Python + Pygame program draws the trace of 4 decaying sine waves, 2 per axis, with rainbow colours. It… read more Spectral Harmonographs

You may have seen those devices at the Science Museum or Exploratorium or Techniquest… There’s a drawing surface and some… read more Harmonograph in Pygame

A variation on the Stars and Stripes American Flag for Independence Day. It’s an exercise in the use of transparency in… read more Stars and Stripes

This little Pygame program paints the Rainbow Flag, as used by the LGBT movement. It illustrates: Importing the Pygame library… read more Rainbow Flag in Pygame

Lindenmayer systems, or L-systems, provide a very powerful way to construct fractals. Lindenmayer used L-systems to describe the behaviour of… read more Drawing Fractals with Lindenmayer Systems

Inspired by this post on Reddit, I wrote this little script to do the same thing. The circle is an… read more A Fake Circle made of Straight Lines

Code Golf is the amusement of writing as short as possible a program to perform a given task. So for… read more Tweetable Python Code Golf

Most Mandelbrot Set programs proceed along the display area, pixel by pixel horizontally, row by row from top to bottom…. read more Fast Mandelbrot Set by QuadTree

Often seen in science museums, the harmonograph is a device that combines wave motions (e.g. from some pendulums) to move… read more Extensible Harmonograph

Graphs (also known as charts) are an indispensible visual aid for conveying a lot of data in an easy-to-digest form…. read more Easy Graph Plotting with Pyplot

A colourful random walk. The basic idea is very simple: choose a random heading in the range 0:360 degrees. Step… read more Random Walk

A very simple Turtle program. Turtle can draw intricate shapes using programs that repeat simple moves. Turtle graphics is a… read more Turtle Star

This is a classic fractal drawn with a recursion algorithm and Turtle graphics. The Sierpinski Triangle’s sides are bisected and… read more Sierpinski Triangle, drawn by a Turtle

This is a very simple introduction to Turtle graphics. The turtle starts in the middle of the window, moves forward… read more Square Spiral

This is your basic Mandelbrot Set plotter. Very little effort made to speed it up, except for plotting top &… read more Naive Mandelbrot Set

This program draws a ‘tree’ by drawing a trunk (initially; later it’s a branch) and appending a tree, recursively. Uses… read more Fractal Tree

Black & White Harmonographs. Because colour gets boring after a while… Harmonographs are those devices often seen in science museums,… read more Black & White Harmonographs

These 3D pictures (except the last) were generated by a Python + Vpython program, translated from Paul Bourke’s C program (which… read more Lorenz Attractor

Benoit B. Mandelbrot  (20 November 1924 – 14 October 2010) was a Polish-born, French and American mathematician, noted for developing a “theory of roughness”… read more Mandelbrot Gallery

These fractals were generated by Python programs from the Active State website. They often make use of recursion. Recursion is… read more Fractal Python Programs

The Buddhabrot is an interesting variation on the well-known Mandelbrot Set, invented by Melinda Green in 1993. It’s a density… read more Buddhabrots – Ghosts of the Mandelbrot Set

Orbits of The Starship Mandelbrot, in 3D. In fractal mathematics, an orbit is the sequence of points in the complex plane… read more Orbits of The Starship Mandelbrot, in 3D