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 …

## 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 …

## 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 …

## 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, …

## 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. …

## 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 …

## 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 Sets

Recall that the Mandelbrot set arises from iterating the complex function z^{2} + 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

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 …

## 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 …