Alan Richmond

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

This is apparently a well-known interview question (but not one I was ever asked). Print the numbers 1 to 100,… read more FizzBuzz

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

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

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

Online 3D Harmonograph This is an online 3d harmonograph version of those harmonograph devices often seen in science museums –… read more Online 3D Harmonograph

The main requirement for a ‘natural fractal’ is that it should look self-similar over a range of scales. That is,… read more Fractals in Nature

Forget Hubble – check out these amazing breath-taking pictures from the Fractal Space Microscope! I made these pictures with JWildfire… read more Astronomy with a Fractalscope

Abstract expressionism is a post–World War II art movement in American painting, developed in New York in the 1940s. It… read more Abstract Fractal Flames

I wish that I could claim these pictures were the result of artistic inspiration after years of starving struggle and… read more Alien Life Forms

Mandrian is a Python + Pygame program to render the Mandelbrot Set  by sub-dividing square areas into sub-squares. If the… read more Mandrian’s Mandelbrot Music

Not fractals – but still, pretty math pictures… These were created with the following Python program (MIT license; download from… read more Spectral Harmonographs

Mandelbrot Zoom sequence up to 1:60,000,000,000, created by Wolfgang Beyer with the program Ultra Fractal 3. Mandelbrot set. Initial image… read more Beyer’s Mandelbrot Zoom

Recall that the Mandelbrot set arises from iterating the complex function z2 + c, where c is a set of… read more Julia Sets

The Burning Ship fractal process is similar to the Mandelbrot Set process, but now the real and imaginary components of z are replaced… read more The Burning Ship

The Mandelbulb is a three-dimensional analogue of the Mandelbrot set, constructed by Daniel White and Paul Nylander using spherical coordinates in… read more 3D Fractals

This is a simple Python program to display the whole Mandelbrot set. Well, not every point from the infinite set,… read more Mandelbrot Set in Python & Pygame

Visiting a web site seems so simple – click on a link in your web browser, and soon – within… read more How the Web works, in Amazing Detail!