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Wikipedia Resources on Fractals

Books on Fractals

Other Resources and Software

Ultra Fractal

Software to create fractals

YouTube animation
A fractal zoom on a Mandelbrot set

Fractal Mathematics
including Types of Fractals

Mandelbrot set

The Mandelbrot Set

Fractals

Quoting from a piece written by Peter Tyson in 2010 on the death of Benoit Mandelbrot, the person regarded as the Father of Fractals:

"Mandelbrot invented the term fractal to describe the "roughness" he saw all around him in nature - the jagged shape of a cloud, the rugged indentations of a coastline. Classical Euclidean mathematics, the kind we learn in school, serves well for the human-made world of straight lines, circles, and squares. But nature's non-linear shapes were generally considered unmeasurable -- until Mandelbrot developed fractal geometry.

"In the whole of science, the whole of mathematics, smoothness was everything," Mandelbrot says in Hunting the Hidden Dimension. "What I did was open up roughness for investigation."

Suddenly, something as ragged as a coastline could come under mathematical scrutiny. While he couldn't actually measure a coastline, Mandelbrot found, he could measure its roughness. It required rethinking one of the basic concepts in math - dimension.

In Mandelbrot's view, another dimension exists between two and three dimensions. It's a fractal dimension, and the rougher something is, the higher its fractal dimension. This roughness, this fractal dimension, he discovered, could be measured quite well using fractal geometry.

Fractals - and a coastline is a fractal, Mandelbrot said - have another distinctive quality: self-similarity. Look at the branches of a tree. Big branches give rise to smaller branches that give rise to yet smaller branches, yet all look essentially the same; they're just at different scales. They're self-similar.

Natural selection, as Mandelbrot pointed out in his classic 1982 book The Fractal Geometry of Nature, has favored fractal self-similarity over and over throughout evolutionary history. From the self-similar stalks on a head of broccoli, to the ever-smaller branching of blood vessels in the human body, fractals are everywhere in nature.

... All told, since Mandelbrot introduced fractal geometry to the world in the 1970s, his new math has informed fields as diverse as biology and physics, ecology and engineering, medicine and cosmology."

~ Peter Tyson writing for Inside NOVA, PBS

Fractal Art

The Fractal Art Manifesto

"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."

"Generating fractals can be an artistic endeavor, a mathematical pursuit, or just a soothing diversion. However, FA is clearly distinguished from other digital activities by what it is, and by what it is not."

  Continue reading ...

Jock Cooper's Fractal Art

Janet Parke Infinite Art

Fractal Art Contests 1997 to 2000