Pretty Math Pictures

Online 3D Harmonograph

This is an online 3d harmonograph version of those harmonograph devices often seen in science museums – except that instead of drawing pretty harmonic patterns on paper, here we plot them in 3D-space! Glowscript code and my …

The main requirement for a ‘natural fractal’ is that it should look self-similar over a range of scales. That is, if you look closer or zoom in, there are shapes similar to what you saw to start with. A tree …

Forget Hubble – check out these amazing breath-taking pictures from the Fractal Space Microscope!

I made these pictures with JWildfire – a free and user-friendly image-processing software, mostly known for its sophisticated flame-fractal-generator.
It is Java-based, open-source and runs on …

Abstract expressionism is a post–World War II art movement in American painting, developed in New York in the 1940s. It was the first specifically American movement to achieve international influence and put New York City at the center of the …

I wish that I could claim these pictures were the result of artistic inspiration after years of starving struggle and demon-haunted torment, but I am an honest man. I clicked a couple of buttons on my computer – occasionally often, …

Mandrian is a Python + Pygame program to render the Mandelbrot Set  by sub-dividing square areas into sub-squares. If the square’s corners all have the same iteration count from the escape function we assume there’s no internal detail to render. …

Not fractals – but still, pretty math pictures… These were created with the following Python program (MIT license; download from GitHub):

You may need to install python and/or pygame, e.g. on Ubuntu/Debian style linuxes:

sudo apt-get install pygame
sudo apt-get …

Mandelbrot Zoom sequence up to 1:60,000,000,000, created by Wolfgang Beyer with the program Ultra Fractal 3.

• Mandelbrot set. Initial image of a zoom sequence: Mandelbrot set with continuously colored environment.
• Coordinates of the center: Re(c) = -.7, Im(c) =

Recall that the Mandelbrot set arises from iterating the complex function z² + c, where c is a set of points in the complex plane. Those values of c for which z, initially zero, remains bounded are in the …

The Burning Ship fractal process is similar to the Mandelbrot Set process, but now the real and imaginary components of z are replaced by their absolute values (i.e. replace – with +):

z_n+1 = (|Re(z_n)| + i …

The Mandelbulb is a three-dimensional analogue of the Mandelbrot set, constructed by Daniel White and Paul Nylander using spherical coordinates in 2009. (wikipedia)

A canonical 3-dimensional Mandelbrot set does not exist, since there is no 3-dimensional analogue of the …