fractal

1975, from Fr., from L. fractus “broken,” pp. of frangere “to break” (see fraction). Coined by Fr. mathematician Benoit Mandelbrot in “Les Objets Fractals.”

“Many important spatial patterns of Nature are either irregular or fragmented to such an extreme degree that … classical geometry … is hardly of any help in describing their form. … I hope to show that it is possible in many cases to remedy this absence of geometric representation by using a family of shapes I propose to call fractals — or fractal sets.” [Mandelbrot, “Fractals,” 1977]

A great place to start learning about Fractals is the Wikipedia entry and an accessible book is The Colours of Infinity

There are a multitude of programs which can be used to create fractal art but the only ones I use are Apophysis and Ultrafractal, so they’re what I’ll talk about. This is in no way intended to be a comprehensive list, but just enough to get people started.

You don’t have to be a mathematician to use any of the most popular fractal programs. If you are, well that can be a great help but being a mathematician doesn’t necessarily mean someone has a good artistic eye, not does having a flair for colour and form in other media mean one will necessarily be accomplished at using fractal software.

APOPHYSIS
This is a free, open source project for producing fractal flames and the latest version can be downloaded from this page

Plugins - which add additional variations to those included in the standard build, are available here

There’s an Apophysis Wiki where you’ll find a lot of information to help you get started.

FracFan - is a really friendly forum where you’ll find lots of people with advice & suggestions, as well as tutorials and parameters to play with.

deviantART has a large and thriving fractal category and is also a source of a huge number of resources. Check out the resource listings at the Apophysis group and at Imager’s Fractal DDs.

I particularly recommend clairejones’s tutorials: very well-written and illustrated.

One of the Apophysis developers has released a 3D hack version which is great fun! Read about it here.

Please don’t automatically discount the older tutorials: many of them include sound advice on the basics of using the program and can be incredibly helpful.

ULTRAFRACTAL
This is available from UltraFractal.com. It’s not, unlike Apophysis, opensource and free but neither is it an expensive piece of software. You can download a full-featured free trial to experiment before you buy (any renders made from an unlicensed copy will be marked “Evaluation Copy”) There is an enormous database of formulae, colouring algorithms and transformations available which are continually being improved and added to and UF includes the capability to layer, mask, and adjust layer blend mode within the program. There’s also (at additional cost) an animation edition of UF.

UF comes with comprehensive tutorials, written by Janet Parke who also teaches the three UF courses at the Visual Arts Academy.

The Ultrafractal group on deviantART has a list of tutorials and walkthroughs and I also recommend the tutorials written by Mary Thornton, Chris Martin and CavalierLady.

BOTH PROGRAMS
I heartily recommend joining the Apo and/or UF mailing lists, depending on your program of choice.

Email apophysis-subscribe@lists.fractalus.com or ultrafractal-subscribe@lists.fractalus.com as appropriate.

Fractalus Information About Fractals Damien Jones’ website, a source of great information.