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 I was too young to go beyond their contemplation (or more clearly, I didn’t care about them very much), but also they were merely beyond my grasp: in that field, a computer was necessary —so I learned— and it would take me some more time to get one. Nevertheless, in the in-between years, my desire to learn, understand and create fractal images never vanished, and now, after several years of having my own computer, and thanks to the Internet, the wait is over.

In May 1998, I began posting some images to the alt.binaries.pictures.fractals newsgroup (abpf, for short), where I found a community of fractals enthusiasts and artists from different parts of the world united by this common bond. Since 05 June 1998, I started *Fractal Division* (later renamed *Third Apex to Fractovia*, and more recently ** Fractal Shots**) to be the home of my pictures and a place where anyone can find links to my favorite spots on the Net. A few days later, I applied and was accepted to the

*Infinite Fractal Loop*, a web ring devoted to this art form.

Most of the images I have on display have been done using *Tiera-Zon*, one of the great freeware fractal generators created by Stephen C. Ferguson. I like this particular generator very much because it is pretty fast and relatively easy to use, and because of its versatility and useful features (it runs on Windows since v. 95). The rest have been done either with any of Stephen’s other generators (especially *Sterling-ware*), with Terry Gintz’s *Fractal ViZion*, Uberto Barbini’s *Fractal Forge* and Olga Fedorenko & Arthur Sirotinski’s *Fractal Explorer*, among others. As it’s obvious, I enjoy using different programs because it helps me, not only to know different techniques and approaches on working with fractals, but also because each one of them has its own gadgets and tricks.

Up to 31 October 1998, I employed an old 486 computer running at 66MHz to create my images. It used to take me quite some time to finish a job, so I avoided deep zooming (otherwise, I might have die in front of the monitor while watching each pixel being painted). That isn’t the case any more (I have a faster computer), so now I’m able to get deeper and deeper in search of some new interesting areas and compositions. Of course, “fastness” is also relative to the fractal generator and the zooming factor. Depending on how deep you go, not even the fastest processor will be able to overcome the complexity of fractals and their iterating processes.

I usually render my fractals at 1600×1200 or 1500×1500 resolution (in some instances even larger) and then apply anti-aliasing to lessen them to 700×525 or 600×600 respectively. This technique has some advantages: it lowers the complexity of the image while yielding a more realistic representation of a fractal’s true appearance, beautifies the ragged edges of highly detailed fractals, and reduces the size of the final file.

I don’t think of myself as an expert fractal artist (there’s a lot to be learn before that, if I ever reach or aspire to reach that point), but I can state some basic “principles” about fractal creation I have realized so far. I have modified and expanded the rest of this article with the idea of giving you more hints on how to start working with fractals in some of the available freeware generators.

- Patience is the keyword. Producing a fractal is a complex process even to a fast computer. Each figure requires a lot of calculations, and those take time. The deeper you go, the slowest the process will be.
- Keep the image relatively small while searching for the area that attracts your creative self (and trying some initial filters), but not under 320×240 pixels or you won’t clearly discern the details. Once you finish working with it, change to a larger resolution for the final file.
- Regularly it will take just a few minutes to generate a fractal image at 1600×1200 pixels, but sometimes it could take as long as several hours or even days (or even a lot more). That depends on the complexity of the fractal, the number of iterations you choose, and your machine’s capacity to handle mathematical computations.
- A small change in the parameters —the values for each variable— will produce an entirely different image. Once you find something interesting, save it or write down the values on paper or to a text file (using NOTEPAD, for example). Otherwise, you will probably be unable to return to that same spot again. You could end up with two dozen fractals before finishing a single image, but you won’t regret it if suddenly an unexpected and unwelcome error happens (and those are common).
- Most fractal generators automatically store a parameters file whenever a bitmap is saved (that’s the case with all of Ferguson’s generators). Some others (FractInt among them) store that information in the same image file; thus, be sure to keep an unadulterated copy of the original file if you’re going to modify the fractal in a graphics editor later. INFI and Kaos Rhei won’t do any of that by default, so get used to do it manually. For INFI, create a new bookmark for every image you come up with; for Kaos Rhei, choose “Save Parameters” from the FILE menu.
- It’s also practically impossible to produce two identical images except when using the same, and only the same, parameters. So keep those files in a save place. They are the the only way you have to reproduce an image later one (if need be) and could be a proof of authorship.
- It is absolutely probable that you won’t know what an image will look like beforehand. You’ll be exploring an imaginary and never-ending world, searching for new vistas to bring to the real one.
- There are certain basic features that are easy to remember and recognize, but while you travel along 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 have been zooming in a region for a while, chances are that you have noticed that several features look washed out, with dark patches and without any detail. It’s just that you are too deep into the figure at a low resolution. Adjust the number of iterations to a higher value and the small Mandelbrots, ridges, spirals, smoothness and spikes will return to view.
- It’s not possible to explore the whole Mandelbrot set in a lifetime, let along all other fractal types out there. Although you can see many fractal images in a lot of publications, web sites and other products (including nature), the chances of getting an original composition are high.
- Most fractal generators are capable of applying filters such as stalks, atan, strands and bubbles to an image. Those are also mathematical expressions that enhance or adds features to these intriguing shapes.
- After getting the figure, concentrate on coloring it. That will make the difference between a regular image and a work worth calling art. The coloring method will depend on the fractal generator you are using. Some of them use color palettes, in which you are free to select the colors to be used; others use color controls, so you just have to move the sliders up or down, left or right, until you get the combination that suits your taste; some use algorithms to give the tones to each pixel; while others are based on predefined color maps, which colors can be rotated in order to change their hues.
- Feel free to apply post-processing techniques to the resulting images. While some purists will say that hurts the natural figure (and that is certainly true), they will add to the creative process, increasing the artistic outcome.
- Study, at least succinctly, the mathematics behind the images. You will discover you don’t need to be a genius to understand the basic concepts. The very process of generating a figure will help you to get some clues that could later turn into wonders.

Juan Luis Martínez

1999.11.19 (Friday) – Updated: 2001.03.11

**Of note (2017.01.03): **

With all probability, some fractal generators mentioned in this article are no longer available or not compatible with 2017 computers anymore, so don’t pay too much attention to the names. Yet, the tips are still true and absolutely valid for today’s programs as they were 15 years ago.