The Very Best Fractal & Mathematical Pictures

This gallery showcases some of our very best fractal & mathematical pictures. Start here! We have Mandelbrot & Julia Sets, Lorenz attractors, The Burning Ship, Flame fractals, Harmonographs, Buddhabrots, Menger Sponges, Sierpinskis, 3D Fractals, Fractal...

Black & White Harmonographs

Black & White Harmonographs. Because colour gets boring after a while… Harmonographs are those devices often seen in science museums, that consist of a pen connected to a number of pendulums, suspended over a sheet...

Lorenz Attractor

These 3D pictures (except the last) were generated by a Python + Vpython program, translated from Paul Bourke’s C program (which has a bunch more pretty pictures). See below for code. The Lorenz system is a...

Mandelbrot Gallery

Benoit B. Mandelbrot  (20 November 1924 – 14 October 2010) was a Polish-born, French and American mathematician, noted for developing a “theory of roughness” and “self-similarity” in nature and the field of fractal geometry to help prove it, which...

Fractal Python Programs

These fractals were generated by Python programs from the Active State website. They often make use of recursion. Recursion is the process of repeating items in a self-similar way. For instance, when the surfaces of...

Buddhabrots – Ghosts of the Mandelbrot Set

The Buddhabrot is an interesting variation on the well-known Mandelbrot Set, invented by Melinda Green in 1993. It’s a density plot of the orbits of points outside the Mandelbrot Set. The Mandelbrot Set is defined as...

Orbits of The Starship Mandelbrot, in 3D

Orbits of The Starship Mandelbrot, in 3D. In fractal mathematics, an orbit is the sequence of points in the complex plane traced out by the iteration of the function that generates the fractal. In the case...

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...

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...

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,...

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...

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...

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...

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...

Mandelbrot Song by Jonathan Coulton

A music video for the song “Mandelbrot Set” by Jonathan Coulton using public domain and creative commons pictures.   Mandelbrot Song Pathological monsters! cried the terrified mathematician Every one of them a splinter in my...

3D Fractal Fly-Throughs

These videos explore some amazing 3d fractal worlds. Take a look, and turn the volume up!     The Mandelbulb is a three-dimensional analogue of the Mandelbrot set, constructed by Daniel White and Paul Nylander...

Mandelbrot Zooms

Mandelbrot Zooms: If you magnified a hydrogen atom to the size of the observable Universe, that would be a magnification of about 1036. Some of these zooms go way way way beyond that…    ...

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)...

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...

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 *...

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...

Fractal Generators

GNU XaoS – GNU XaoS Fractalnow – A fast, advanced, multi-platform fractal generator. FractalNow provides users with tools to generate pictures of various types of fractals quickly and easily. It is made of both a...