## Fractals

What are Fractals?

Benoit Mandelbrot,
The father of fractal geometry

Definitions:
Fractals: A geometric pattern that is repeated (iterated) at ever smaller (or larger) scales to produce (self similar) irregular shapes and surfaces that cannot be represented by classical (Euclidian) geometry. Fractals are used especially in computer modeling of irregular patterns and structures found in nature.

Computer generated and a Fractal found in nature

Iteration: The process of repeating a set of instructions a specified number of times or until a specific result is achieved. Relative to this art form, fractals are a unique art form using mathematical formulas to create art with an infinite diversity of form, detail, color and light. In simple terms, a fractal is a graphical image that represents the behavior of a mathematical equation.

The formula used determines how each pixel in an image is formed and colored. (Pixels are the smallest display elements that make up the images you see on a computer monitor or television.) A typical fractal image contains millions of these pixels. These complex images of extraordinary beauty can arise out of fairly simple mathematical functions and then by selectively modifying these formulas, changing coloring algorithms etc. one can create unique compositions previously unseen to the human eye.

changing formulas produce the unique design and coloring

In the broader scientific sense, they are essentially geometric shapes or forms that are represented in natural objects, from a fern leaf or tree, to a spider web or snowflake, to larger phenomena such as clouds or even galaxies in space.

What is unique about fractals? One major aspect, infinity! A fractal is infinite in two distinct senses, the macro and the micro. Firstly, it extends to infinitely large values of the co-ordinates, ie; outwards in all directions from the center. Secondly, it has infinite detail in that one can zoom (magnify) in or out without limit (at least in theory) to show ever finer detail. This feature is one of the key aspects of fractals, whether relative to exploring fractals as an art form or as found in nature.

Another feature, which distinguishes a fractal image, is its property of self-similarity; an arbitrary region of a fractal looks similar (but not necessarily identical) to the entire fractal. Thus, fractals are analogous to DNA: just as all the information for a living organism is contained in its DNA, so does a small region (as small as you’d like!) contain all the information for the “parent” image.

Fractals, in art and nature, can range from beautiful symmetry to the chaotic, from a perfectly symmetrical snowflake to a massive chaotic thunderhead cloud. But regardless of their symmetry or level of chaos fractals are everywhere we look and I hope the beauty of fractal art captivates your imagination!

looks like a child’s kaleidoscope