About My Fractals

What are fractals? Fractals are a form of computer generated art. They contain complex, repetitive, mathematically based shapes and patterns that resemble those found in nature. The word "fractal" also means an algorithm or shape, characterized by patterns repeated at every scale (self-similarity). "Fractal" also means the branch of mathematics named and explored by Benoit Mandelbrot.

Why are fractals important? "Clouds are not spheres, mountains are not cones, coastlines are not circles and bark is not smooth, nor does the lightning travel in a straight line." - Benoit Mandelbrot

Before Mandelbrot and fractals, scientists estimated or measured real world phenomena by treating them like traditional or classic geometric shapes like spheres, cones, circles and lines. These provided rough approximations that were useful even if not wholly accurate. Trying to accurately represent the real phenomena mathematically became impossibly complex very fast. The calculations were referred to as "messy" and scientists contented themselves with their approximations. The natural world was considered "messy." Maybe scientists didn't believe that a perfect world would only consist of classical geometric shapes but they acted that way.

Then in the 1960s Benoit Mandelbrot started studying self-similarity in a number of papers. In 1975 he coined the term "fractal," short for fractional dimension. He illustrated this mathematical definition with striking computer-constructed visualizations. These images captured the popular imagination and led to the popular meaning of the term "fractal" as used in the artwork around you.

What was so important to science was that fractal mathematics could be used to much more accurately estimate, measure and predict real world phenomena for the first time. It turned out that fractal behavior was all around us! Fractal behavior has been found in:

How are fractals made? Fractals are made using computers. They are mathematically based and require significant amounts of computer processing time. For most of my fractals I use a program called Ultra Fractal. It allows me to create fractals, zoom in on them, color them, mathematically reprocess them, combine multiple images, create new fractal formulas, create new coloring formulas and more. Ultra Fractal has a wonderful set of tools for working with fractal images. My flame fractals are made with a program called Apophysis. It is not as developed or versatile as Ultra Fractal but it is specially made to work with flame fractals. Fractals can be printed with color laser printers, high-end inkjet printers or high-end photo printers.

How long does it take to make a fractal? When I started in 1988 we were still using 8 MHz 8088 PCs. It took awfully long for the PC to generate a small image. Sometimes we would let the PC run for days to generate a full screen image. Today's PCs are immeasurably faster. Most full screen images take only seconds to create and never take more than a few minutes. However, now I render images for printing 24" x 30" posters at 300 dots per inch resolution. These images are much larger than a full screen. They can take from 30 minutes to several hours to several days to produce on today's PCs.

Why do you create fractals? I love the brilliant colors and evocative images. Yes, the math, science and computer programming are interesting, but it is the images themselves that draw me. When I "discover" a new fractal my spirit gives a little leap for joy. I guess it is kind of a spiritual experience. Sometimes their beauty takes my breath away. The only thing better than that is sharing them with someone else who has a similar experience. What could be better than creating art that makes peoples' spirits leap for joy?

I also am a photographer. Creating fractals is a little like landscape photography. Instead of exploring the natural world with my camera, I use my PC to explore worlds that exist in mathematical formulas. I have a little more artistic license creating fractals than I would with landscape photography. No one has seen with their own eyes the mathematical landscapes I explore. The coloring and certain other attributes are arbitrary. My fractal creations are windows into these mathematical landscapes. I like being an explorer of mathematical landscapes and I especially like sharing my journeys in those worlds with all of you!

How long have you been making fractals? I have been creating fractals for over 20 years. I got my first fractal program at a computer conference in 1988. I typed in the program and was fascinated by the images. The images were much simpler back then since the PCs of the time took quite a bit of time just to fill the screen with one image. I started modifying the program and making it my own. After awhile adding new features became more and more complex. In 1990 I discovered the program Fractint. Fractint was a collaborative project involving more contributors that I can count and best of all it was free. It had more features than I could ever have hoped to program myself, supported many types of fractals and ran much faster so I abandoned my program and started using Fractint. I did a couple of exhibits in the 1990's and sold some artwork. As I started running into various limitations with Fractint however I started doing fewer and fewer new fractal creations.

In 2004 I discovered Ultra Fractal. I started creating new fractals again as I explored its impressive capabilities. By 2005 I was building quite a collection of new fractals and was getting positive feedback from friends and coworkers. I thought about doing an exhibit but I hadn't really had good experiences with exhibits. People liked my work but few bought large framed prints. In the end exhibits ended up costing me more than I took in. Then I decided to publish a fractal calendar. My first calendar, Fractal Fantasies 2006, was a very popular gift item. I sold out of my limited run and made a nice little profit.
I then took some classes on using Ultra Fractal from Janet Parke, a well-known fractal artist. Those classes helped me dive deeper into Ultra Fractal's abilities and start working more seriously on the artistic side. Although the images in my 2006 calendar were new and interesting they were purely fractal. My newer artwork is based on fractal images but also use multiple layers, masking, color formulas and other tools to make them even more interesting.

I have published five fractal calendars: Fractal Fantasies 2006, Fractal Festivity 2007, Contemplating Chaos 2008, Ancient Fractal Arts 2009 and now Fractal Genesis 2011. My Fractal Genesis 2011 calendar is available for sale on this website.

Where are the originals? Unlike a painting or a piece of sculpture, there are no "original" fractal prints. Since each print produced is at the same quality as all the other prints, you could say that all fractal prints are originals. I am selling my fractals as limited editions of 100 prints. Print 1 is the same as print 100 but for art collectors low numbered prints are more highly valued.