Extending the Chaos Game: Determinism and DNA

HIV Color Game

I recently came across some interesting variations and applications of the Chaos Game.

One version is located at the Boston U web site and is credited to Johanna Voolich and Robert L. Devaney. Their version is very unique twist on the Game - instead of the randomness that forms the basis of the Game, they have replaced the randomness with a strictly deterministic game. In their version, the player tries to get a random starting point into a specific target area of the Sierpinski triangle by choosing a series of half-way jumps to specific vertices. The "winner" of the gme is the one who reaches the target area in the fewest number of jumps. (Click here to play the game on-line.)

An even more fascinating Chaos Game comes from Dan Ashlock at Iowa State University, where he uses a 4-cornered Chaos Game to display the sequence of bases in DNA molecules. (The image at the top of this post is from a segment of HIV DNA.) In this Chaotic Game of Life, points are drawn half-way to vertices depending on the next base in the DNA strand. The pictures look remarkably similar to playing the Chaos game randomly! See Ashlock's website for a set of images from different organisms, as well as some Markov chain models that help explain and interpret the images.

Melt-O-Waves

The fractal image appearing in the site header was produced using Ultra Fractal 3.05. The original image was designed by Damien M. Jones in 1999, and published to the Ultra Fractal Formula Database

Click to enlargeThe image is titled Melt-O-Waves. I varied the colors, zoom factor, layer blending method, and starting values for the underlying Mandlebrot set.

Please visit fractalus - this is an amazing site of fractal art that is managed by Damien Jones.

Fractal Image Generation, Part 1

The fractal images generated for this blog have been generated using UltraFractal 3.05 - an incredibly robust package that is effectively the PhotoShop of the fractal kingdom.

In addition to all possible types of mathematical settings, UltraFractal allows layering (as in PhotoShop), with different blending styles adjustable (e.g. addition, difference, hue, etc.) The interface allows the designer to create or edit fractal formulas, set up color palettes, and add mathematical image transformations. There are many pre-loaded fractal types loaded - even with these you will have days of exploration as you vary coloring schemes and learn layering with fractals.

There is also a very active user group that uploads new fractal parameter files and color templates - all available for download. You can find appropriate links, and much more at Janet Parke's Ultra Fractal Resource Page.

The result is a degree of image control that is state of the art.

UltraFractal also contains a rendering engine with anti-aliasing for producing high-quality images for web and print applications.

You can try UltraFractal free for a brief period.

Note that ChaosPro is almost as powerful as UltraFractal and is freeware! Check it out!

For a good source of chaos and fractal links check out third.apex.to.fractovia by Juan Luis. This is a very nice site, and Juan is clearly interested in the fractal aesthetic:

Have in mind that this site, third.apex.to.fractovia, focuses on the artistic side of fractals, not in their mathematical aspects, so these applications are primarily intended for picture or music creation, not for studying fractals as mathematical models or for in-depth experimentation (what most of them can do in any event).

Note that some of the software generates fractal music.

Is Fractal Art Really Art?

Originally Posted by Jeremiah Noll

"grassyknoll"
"orangefla"
"hazyire" Fractal art is a controversial matter, but what in the art world isn't controversial? Contrary the opinions of some dissenters fractals are not easy to make, there are infinite possibilities, it takes a great deal of talent, and it is in no way cheating. Fractal art is an innovative art form and it will likely be the next art fad. Some of the greatest art was at some time controversial.

The fractal software on the web that I recommend is Sterling Fractal Generator, Chaos Pro, and Terragen.

These are also free and can be downloaded with little trouble. You can also check out the fractal portion of my website.

By the way they are both unreal.