Friday, 13 July 2012

Fractal Art

A fractal is defined as: "a geometrical or physical structure having an irregular or fragmented shape at all scales of measurement between a greatest and smallest scale such that certain mathematical or physical properties of the structure, as the perimeter of a curve or the flow rate in a porous medium, behave as if the dimensions of the structure (fractal dimensions)  are greater than the spatial dimensions."

But what the definition fails to mention is that fractals, as well as being mathematical or physical, are an art form in themselves.

To be honest writing about fractals is kind of pointless. The best way to experience fractals is to get down and dirty with them. There are hundreds of software titles that will allow you to not only view fractals but also create them. Below is a few of the software titles I have used; either presently or in the past.

GnoFract 4D (Linux/Mac) (Free/Open Source): Gnofract 4D is a free, open source program which allows anyone to create beautiful images called fractals. The images are automatically created by the computer based on mathematical principles. These include the Mandelbrot and Julia sets and many more. You don't need to do any math: you can explore a universe of images just using a mouse.

Xaos (Linux/Mac/Windows) (Free/Open Source): XaoS is an interactive fractal zoomer. It allows the user to continuously zoom in or out of a fractal in a fluid, continuous motion. This capability makes XaoS great for exploring fractals, and it's fun! If you don't know what fractals are, don't worry. XaoS includes many animated tutorials that make learning about fractals fun and easy. These tutorials are also a great introduction to all of XaoS's features.

Fractint (Linux/Windows/DOS) (Free): Fractint is a freeware fractal generator created for IBMPC's and compatible computers to run under DOS and ported to Linux. It has many great features and it is still being upgraded and improved by the Stone Soup team.

Ultra Fractal (Mac/Windows) ($49): With Ultra Fractal, you can choose from thousands of fractal types and coloring algorithms, zoom in as far as you want, use gradients to add color, and apply multiple layers to combine different fractals in one image. Ultra Fractal is very easy to use. No mathematics required!

Gnofract 4D and Xaos are the two I currently use; and have been for the last few months. I tried the Linux version of Fractint but found that the DOS version running in a DOS Box worked better than the Linux version (although, admittedly, that might have just been me). Ultra Fractal I have not used for ages. But I have kept up with how the software has developed and the newer versions are great pieces of software.

So what does a fractal look like? As a formula (in Xaos) it will look somewhat like this:


This is the code, well part of it, that makes this fractal:

But the good news is that you don't have to know anything about equations to start designing fractals. Just take an already existing one and edit it to see what the output is.

Changing z^2+c to z^2+c^(z+c) gives a whole different fractal:

But the Mandelbrot set is merely one fractal out of hundreds of millions. And as I said before the best way to see exactly what can be done with fractals is download software and dive in.


  1. Just a quick addition ... Someone suggested Mandelbulb 3D which is a Windows program. It runs fine in Ubuntu under WINE.

    You can get it here:

    And I rendered a fractal called "Real Power" in 5 minutes 41 seconds which can be seen here:

    A nice piece of software.

  2. My suggestion for your “Real Power” fractal is to transform it into “Real Power” food: blanch it for 5 min. and 41 sec. in plenty of boiling, salted water and serve it with brown butter and grated Parmesan.

    (I don’t mean to confound the statistics, but I don’t only spend this one hour eating per day, I spend a lot of time thinking about eating. LOL)


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