Just What are Fractals?

I get alot of questions about “What do you mean you make Fractals? What are Fractals? Are Fractals really a Art Form?” Well here is a Paper I wrote that I hope may explain some of the mystery surrounding Fractals and you can tell me what you think…….I hope you find it helpful. If you have any questions or need more info,Please contact me.

What Are Fractals?

From sea shells and spiral galaxies to the structure of human lungs, Veins, leaves branches, cauliflower, rivers, lighting, mountains, brain, snowflakes, salt the patterns of chaos are all around us but may have never noticed them.

Fractals are patterns formed from chaotic equations and contain self-similar patterns of complexity increasing with magnification. If you divide a fractal pattern into parts you get a nearly identical reduced-size copy of the whole.

The mathematical beauty of fractals is that infinite complexity is formed with relatively simple equations. By iterating or repeating fractal-generating equations many times, random outputs create beautiful images.Fractals are also recursive, regardless of scale. Ever go into a store’s dressing room and find yourself surrounded by mirrors? For better or worse, you’re looking at an infinitely recursive image of yourself.

Most of us grew up being taught that length, width and height are the three dimensions, and that’s               that. Fractal geometry throws this concept a curve by creating irregular shapes in fractal dimension; the fractal dimension of a shape is a way of measuring that shape’s complexityrns that are unique, yet recognizable.

Early African and Navajo artists noticed the beauty in these recursive patterns and sought to emulate them in many aspects of their everyday lives, including art and town planning

. As in nature, the number of recursive iterations of each pattern was limited by the scale of the material they were working with. Leonardo da Vinci also saw this pattern in tree branches, as tree limbs grew and split into more branches

. In 1820, Japanese artist Katsushika Hokusai created “The Great Wave Off Kanagawa,” a colorful rendering of a large ocean wave where the top breaks off into smaller and smaller (self-similar) waves

.Mathematicians eventually got in on the act as well. Gaston Julia devised the idea of using a feedback loop to produce a repeating pattern in the early 20th century. Georg Cantor experimented with properties of recursive and self-similar sets in the 1880s, and in 1904 Helge von Koch published the concept of an infinite curve, using approximately the same technique but with a continuous line. Lewis Richardson exploring Koch’s idea while trying to measure English coastlines. Unconventional 20th century mathematician Benoit Mandelbrot created the term fractal from the Latin word fractus (meaning irregular or fragmented) in 1975. As a genre, Fractal Art (FA) has been around for only approximately 15-20 years. Its first major public display may be considered to be an article about the Mandelbrot Set published in “Scientific American” in 1985. Since then, many advances have been made, both in fractal rendering capabilities and in the understanding of fractal geometery. These irregular and fragmented shapes are all around us. At their most basic, fractals are a visual expression of a repeating pattern or formula that starts out simple and gets progressively more complex. Lacking at the time was a machine capable of performing the grunt work of so many mathematical calculations in a reasonable amount of time to find out where these ideas really led. As the power of computers evolved, so too did the ability of mathematicians to test these theories.

Fractals as Art

Fractal Art is a genre concerned with fractals—shapes or sets characterized by self affinity (small portions of the image resemble the overall shape) and an infinite amount of detail, at all scales. Fractals are typically created on a digital computer, using an iterative numerical process. Lately, images that are not technically fractals, but that share the same basic generating technique and environment; have been welcomed into the Fractal Art world.

Fractal Art is a subclass of two dimensional visual art, and is in many respects similar to photography—another art form which was greeted by skepticism upon its arrival. Fractal images typically are manifested as prints, bringing Fractal Artists into the company of painters, photographers, and printmakers. Fractals exist natively as electronic images. This is a format that traditional visual artists are quickly embracing, bringing them into FA’s digital realm.

Fractal Art is not:

Computer(ized) Art, in the sense that the computer does all the work. The work is executed on a computer, but only at the direction of the artist. Turn a computer on and leave it alone for an hour. When you come back, no art will have been generated.

Random, in the sense of stochastic or lacking any rules. Being based on mathematics, fractal rendering is the essence of determinism. Apply the same image generation steps, and the same result will follow. Slight changes in process usually lead to slight changes in product, making Fractal Art an activity which can be learned, not a haphazard process of pushing buttons and turning knobs.

Random, in the sense of unpredictable. Fractal Art, like any new pursuit, will have aspects unknown to the novice, but familiar to the master. Through experience and education, the techniques of  Fractal Art  can be learned. As in painting or chess, the essentials are quickly grasped, although they can take a lifetime to fully understand and control. Over time, the joy of serendipitous discovery is replaced by the joy of self-determined creation.

Something that anyone with a computer can do. Anyone can pick up a camera and take a snapshot. However, not just anyone can be an Ansel Adams or an Annie Liebovitz. Anyone can take brush in hand and paint. Not just anyone can be a Georgia O’Keeffe or a Pablo Picasso. Indeed, anyone with a computer can create fractal images, but not just anyone will excel at creating Fractal Art.

Fractal Art is:

Expressive. Through a painter’s colors, a photographer’s use of light and shadow, or a dancer’s movements, artists learn to express and evoke all manner of ideas and emotions. Fractal Artists are no less capable of using their medium as a similarly expressive language, as they are equipped with all the essential tools of the traditional visual artist.

Creative. The final fractal image must be created, just as the photograph or the painting. It can be created as a representational work, and abstraction of the basic fractal form, or as a nonrepresentational piece. The Fractal Artist begins with a blank “canvas”, and creates an image, bringing together the same basic elements of color, composition, balance, etc., used by the traditional visual artist.

Requiring of input, effort, and intelligence. The Fractal Artist must direct the assembly of the calculation formulas, mappings, coloring schemes, palettes, and their requisite parameters. Each and every element can and will be tweaked, adjusted, aligned, and re-tweaked in the effort to find the right combination. The freedom to manipulate all these facets of a fractal image brings with it the obligation to understand their use and their effects. This understanding requires intelligence and thoughtfulness from the Artist.

Most of all, Fractal Art is simply that which is created by Fractal Artists: ART. © 1999 Kerry Mitchell

I’m an East Coast based artist who seeks to utilize various harmonies and ideas to visually engage the audience.  I also use my art as an opportunity to experiment with the range of possibilities allowed through my choice of materials and software.

My work captures spaces of partial or full illumination between the perfect shadows on all sides of a person or an object.   The viewer is able to appreciate the simplicity, splendor and exquisiteness of my work and the subject. I believe that the quality of the actual work is what is most important.

Melissa Messick ** Lion6255@aol.com ** 804-739-5312 ** Central Virginia