Though I have been doing fractals for not too long a time, their intriguing shapes have fascinated me since I saw one of these figures in the pages of a science-related magazine in the late 1980s. Back then, not only was I too young to go beyond simple admiration (or more precisely, I didn’t care all that much), but they were also out of reach: in that field, a computer was necessary —so I learned— and it would be some time before I could get one. Nevertheless, in the in-between years, my desire to learn, understand and create fractal images never faded, and now, after several years of owning a computer, and thanks to the Internet, the wait is finally over.
In May 1998, I began posting images to the alt.binaries.pictures.fractals newsgroup (abpf, for short), where I discovered a community of fractals enthusiasts and artists from around the world united by this common bond. On 05 June 1998, I started Fractal Division (later renamed Third Apex to Fractovia, and more recently Quaint Symmetries) as the home for my pictures and a hub where visitors could find links to my favorite spots on the web. A few days later, I applied to and was accepted into the Infinite Fractal Loop, a web ring dedicated to this art form.
Most of the images I have on display were generated in Tiera-Zon, one of the great freeware fractal generators developed by Stephen C. Ferguson. I’m especially fond of this program because it’s pretty fast, relatively easy to use, and quite versatile, with a range of useful features (it runs on Windows since version 95). The rest were made either with any of Stephen’s other generators (especially Sterling-ware), Terry Gintz’s Fractal ViZion, Uberto Barbini’s Fractal Forge, or Olga Fedorenko & Arthur Sirotinski’s Fractal Explorer, among others. As it’s obvious, I enjoy working with different programs because it helps me to know different techniques and approaches on working with fractals, but also because each generator has its own tricks.
Until 31 October 1998, I was using an old 486 computer running at 66MHz to create my images. Rendering took quite a bit of time, so I avoided deep zooming —otherwise, I might have die in front of the monitor watching each pixel being painted. That’s no longer the case —now I have a faster computer, so I’m able to get deeper and deeper in search of new interesting areas and compositions. Of course, speed is also relative to the fractal generator and the zoom level. Depending on how deep you go, not even the fastest processor can overcome the complexity of fractals and their iterative processes.
I often render my fractals at up to 8000×6000 resolution and then apply anti-aliasing to lessen them close to 1280×960. This technique has several advantages: it decreases the visual complexity of the image while producing a more realistic representation of a fractal’s true appearance, smooths out the ragged edges in highly detailed fractals, and reduces the size of the final file.
I don’t consider myself a fractal artist (there’s still much to learn before I can claim that, if I ever aspire to it), but I can share some basic “principles” of fractal creation I have come to understand so far. I have modified and expanded the rest of this article with the aim of offering some hints on how to get started working with fractals using some of the available freeware generators.
- Patience is the key. Producing a fractal is a complex process even for a fast computer. Each figure requires a lot of calculations, and those take time. The deeper you go, the slowest the process becomes.
- Keep the image relatively small while searching for the area that appeals to your creative self (and trying out some filters), but avoid going below 320×240 pixels, as you won’t be able to discern the details, Once you have the basic look, switch to a larger resolution for fine-tuning before going for the final rendering.
- Typically, it takes a few minutes to generate a fractal image at 1600×1200 pixels, but sometimes it can take much longer —even several hours or days (no kidding). That depends on the complexity of the fractal, the number of iterations selected, your machine’s processing power, and the final image size.
- A small change in the parameters —the values assigned to each variable— will produce an entirely different image. Once you find something interesting, save both the image and the parameters files, or copy the values into a text file (using NOTEPAD, for example). Otherwise, you won’t be able to return to that same spot again. You might end up with two dozen fractals before completing a single image, but you won’t regret it if an unexpected and unwelcome error happens —and those are common.
- Most fractal generators automatically store a parameters file whenever an image is saved. That’s the case with all of Ferguson’s generators for example. Others, like FractInt, embed that information within the image file itself; therefore, be sure to keep an unaltered copy of the original file if you plan to modify the fractal later in a graphics editor. INFI and Kaos Rhei don’t do this by default, so get used to do it manually. For INFI, create a new bookmark for every image you generate; for Kaos Rhei, select “Save Parameters” from the FILE menu. In some cases, saving both a bitmap and a parameters file is essential: one won’t work without the other.
- It’s practically impossible to produce two identical images unless you use the exact same parameters. So keep those files in a safe place —they are the only way to reproduce an image later on (if needed) and may serve as proof of authorship.
- It’s entirely possible that you won’t know what an image will look like beforehand. You’ll be exploring an imaginary and never-ending world, searching of new vistas to bring to the real one.
- There are certain basic features that are easy to remember and recognize, but as you travel through the Mandelbrot regions, for example, new patterns never seeing before will come into view. That’s part of the thrill that attracts us to fractal art.
- If you’ve been zooming in a region for a while, you may have noticed that certain features start to look washed out, with dark patches and a lack of detail. It usually means you’re too deep into the figure at a low resolution. Increase the number of iterations, and the small Mandelbrots, ridges, spirals, and spikes will return to view.
- It’s not possible to explore the entire Mandelbrot set in a lifetime, let along all the other fractal types out there. Although you can find countless fractal images in a lot of publications, websites and other platforms, the chances of creating an original composition are high.
- Most fractal generators can apply filters such as stalks, atan, strands and bubbles to an image. These are also mathematical expressions that enhance or adds features to these intriguing shapes.
- After generating the figure, focus on coloring it —this is the difference between a regular image and a work worthy of being called art. The coloring method depends on the fractal generator you are using. Some use color palettes, allowing you to freely select the colors; others use color controls, where you adjust the sliders to get a combination that suits your taste, Some rely on algorithms to assign tones to each pixel, while others are based on predefined color maps, which can be rotated to shift hues.
- Feel free to apply post-processing techniques to the resulting images. While some purists may argue that this compromises the natural figure (and that’s true to some extend), that can enhance the creative process and elevate the artistic outcome.
- Study, even succinctly, the mathematics behind the images. You’ll find out that you don’t need to be a genius to understand the basic concepts. The very process of generating a figure will provide clues that may later lead to wonders.
Juan Luis Martínez
1999.11.19 (Friday) – Updated: 2001.03.11
Of note (2017.01.03):
Some fractal generators mentioned in this article are no longer available or are not compatible with today’s computers, so don’t pay too much attention on the names. However, the tips are still valid and applicable to current programs, just as they were in the past.
Revised on 2025 April 18 for clarity.