Posted in 3D Harmonograph

Online 3D Harmonograph

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 …

Posted in Natural

Fractals in Nature

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 …

Posted in Flame

Astronomy with a Fractalscope

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 …

Posted in Flame

Abstract Fractal Flames

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 …

Posted in Flame

Alien Life Forms

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, …

Posted in Mandelbrot Program

Mandrian’s Mandelbrot Music

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. …

Posted in Harmonograph Program

Spectral Harmonographs

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 …

Posted in Mandelbrot Zoom

Beyer’s Mandelbrot Zoom

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) =
Julia Set
Posted in Julia Set

Julia Sets

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 …

Burning Ship
Posted in Fractal

The Burning Ship

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 +):

zn+1 = (|Re(zn)| + i …

Posted in 3D

3D Fractals

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 …

Posted in Mandelbrot Program

Mandelbrot Set in Python & Pygame