A fractal is an object that display self-similarity at various scales. In other words, if we zoom in any portion of a fractal object, we will notice the smaller section is actually a scaled-down version of the big one. Another very important aspect of a fractal is that it has a fractional dimension. Fractals are produced by iteration (the repetition of the same process).
Benoît Mandelbrot defines a fractal as “A rough or fragmented geometric shape that can be subdivided in parts, each of which is (at least approximately) a reduced-size copy of the whole.”
Learn more about fractals
Fractal (available in other languages)
- Evgeny Demidov (Comp.)
The Mandelbrot and Julia sets anatomy (available in Russian)
- Yale University
Sec. 3: Basic information about fractals
- Junpei Sekino
Sekino’s Fractal Gallery
- Paul Bourke
An Introduction to Fractals
Fractals and Computer Graphics
- Fabio Cesari
- Glenn Elert
The Chaos Hypertextbook
- Paul Derbyshire
Quick Guide to the Mandelbrot Set
- David G. Green
Fractals and Scale
A Sense of Scale
- NOVA-PBS – John Briggs
The most famous fractal
History of fractals
The term fractal art applies mainly to a form of digital abstract art that seeks to reflect and emphasize the eternal expressions of order and chaos that permeates Nature’s structures and behaviors as well as the intricacies of humanity through the use of self-similar patterns and shapes. Although artists have been using self-repeating designs since time immemorial, this new form of algorithmic art chooses fractal geometry functions and the computational capabilities of the computer as its tools for the creation of infinitely detailed or stunningly simple forms that reveal and enhance the fantastic visions that comes from the realm of numbers.
Emerging from the studies of fractal geometry in the last third of the twentieth century and the popularity of the microcomputer in the 1980s, it rapidly evolved throughout that decade, and especially in the 1990s, thanks to the development of faster processors and the advent of the Internet as a medium of mass communication. –This paragraph is part of the Fractat-Art FAQ.
Many things have been said about the artistic value of fractal images. The matter is far from settled.
Jean-Pierre Louvet, Juan Luis Martínez & Phil Jackson (maintainers)
Note: Old document. Some links are broken, but the information is still good and valid.
- Fractal art
- Fractal art
- Charles Vassallo
Fractals as Art
- See more related discussions and links HERE
Information in other languages
If your main language is not English, here are a few sites with fractal information in other languages. French and Spanish to begin with (I hope there will be more to add in the near future).
Fractale (autres langages)
- Jean-Pierre Louvet
Les fractales, une curiosité mathématique
- Charles Vassallo
Art et fractales
Fractal (disponible en otros idiomas)
- Íñigo Quílez
De la dinámica a la geometría en el conjunto de Mandelbrot
- Miguel A. Sierra
- Ariel Osvaldo Quezada
Fractales, más allá de 1D, 2D o 3D
- Juan Luis Martínez
Naturaleza de los fractales
- Miguel Reyes
- YouTube – Traducción de video de NOVA
El mundo de la geometría fractal
Theory and application
Beyond the graphics, fractal geometry and its related fields have produced a great variety of studies and perspectives that addresses every imaginable topic of human knowledge and the natural and philosophical domains.
- School of Wisdom
- Steven Mason
Fractal Logic: The art of science and the science of art