By definition a fractal is an object or quantity that displays self-similarity, in a somewhat technical sense, on all scales. The object need not exhibit exactly the same structure at all scales, but the same "type" of structures must appear on all scales.
Fractals are common in nature (clouds, plant structures, leaves on a tree, flowers, ripples on a pond are some examples) Broccoli is an excellent example of a fractal image as each unit repeats the larger structure in a similar manner (not identical, but similar).
A number of years ago I was introduced to the idea of fractals and spent time exploring them. Most of my products have been done using fractal generator software, printing out the image on fabric and then sewing and beading the fabric. But..fractal images can be drawn on paper, either from imagination or from observations of nature.
Several fabric artists use fractal images such as Carol Bryer Fallert, Rose Rushbrook and Gail Garber and have web sites to explore, especially Rose Rushbrook’s site. Both Carol and Gail use expanding and contracting streams of triangles and Carol’s web site sells a method for creating these streams.
I was able to take a class at www.quiltuniversity.com from Lily Kerns where I learned how fractals can be developed on one’s own and had a brief introduction to software programs to generate fractals. The class called: Fractal Fragments is still available at Quilt University and theirofferings are available to anyone with access to a computer.
Many fractal generating programs are available for use on a PC. Ultrafractal and an offshoot: Apothesis are my favorites. There are fewer programs for IMac but I now am using XaoS which is a free download however previous fractal knowledge with a PC program will enable you to create more images with its use.
An online art academy :visual-arts-academy.com offers classes in fractal generation and Rose Rushbrook’s blog offers information about how she works with fractals. There are probably many other sites that can be Googled using the words “fractal images” , fractal generation, and other “fractal terms”
Once the fractal image is finished it can be saved or printed on paper or fabric. I like to manipulate the effects in Adobe PSE to get the best and brightest, sharpest image and then print on special paper or silk fabric.