A fractal is an object that displays self-similarity at various scales. In other words, if we zoom in on any portion of a fractal object, we will notice the smaller section is actually a scaled-down version of the bigger one (to some extend). Another very important characteristic of a fractal is that it has fractional dimension. Fractals are generated by iteration —the repetition of a process, where the outcome of a step becomes the input for the next.
Learn more about fractals
- Mark McClure
Chaos and fractals - Wikipedia
Fractal (available in many languages) - Evgeny Demidov (Comp.)
The Mandelbrot and Julia sets anatomy (available in Russian) - Yale University
Fractal Geometry - Fractal-Art-FAQ
Sec. 3: Basic information about fractals - Junpei Sekino
Sekino’s Fractal Gallery - Paul Bourke
An Introduction to Fractals
Fractals and Computer Graphics
Fractals, chaos - Fabio Cesari
Fractal Explorer (old Geocities backup) - Glenn Elert
The Chaos Hypertextbook - Paul Derbyshire
Quick Guide to the Mandelbrot Set (currently unavailable) - NOVA-PBS
A Sense of Scale - NOVA-PBS – John Briggs
The most famous fractal
History of fractals
- NOVA – PBS
A radical mind: Interview with Benoît Mandelbrot (2005)
Fractal art
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 quote is part of the Fractat-Art FAQ.
Much have been said about the artistic value of fractal images, but the matter is far from settled.
Fractal art
- Fractal-Art-FAQ
Jean-Pierre Louvet, Juan-Luis Martínez & Phil Jackson (maintainers)
Note: Old document. Most links are broken, but the information is still valid. - Fractal art
Wikipedia - Fractal art
arthistory.net - Charles Vassallo
Fractals as Art (currently unavailable) - See more related discussions and links HERE
Information in other languages
If English is not your first language, here are a few sites with information in other languages.
Français
- Wikipédia
Fractale (autres langages) - Jean-Pierre Louvet
Les fractales, une curiosité mathématique - Charles Vassallo (currently unavailable)
Art et fractales
Español
- Wikipedia
Fractal (disponible en otros idiomas) - Javier Barrallo Calonge
Geometría fractal: algoritmos y creación artística - Miguel A. Sierra
área fractal - Ariel Osvaldo Quezada
Fractales, más allá de 1D, 2D o 3D (PDF) - Juan-Luis Martínez
Naturaleza de los fractales (explicación sencilla) - Miguel Reyes
Fractales (PDF) - El Blog de Alerce
El arte fractal y la Teoría del Genio - El Arte Hoy
Artistas emergentes en el fascinante mundo del arte fractal - YouTube – Traducción de video de NOVA
El mundo de la geometría fractal - Jonathan Ramírez Polo
Una mirada artística a la geometría fractal en contextos escolares (PDF) a través de la
propiedad de la auto semejanza en grado 9º de la Educación Básica en Colombia. - Javier Barrallo Cologne
Geometría fractal: algoritmos y creación artística
Theory and application
Beyond graphics, fractal geometry and its related fields have inspired a wide range of studies and perspectives that touch on nearly every area of human knowledge, including the natural and philosophical domains.
English
- School of Wisdom
Fractal Chaos
Español
- Manu Martín
Fractalina