For the layman, the adventure of fractal pictures begins with the
Very hard mathematics are hidden behind the Mandelbrot Set, but you can completely ignore them if you are interested only in the beauty of pictures. Many user-friendly programs now exist that allow you to get pictures comparable to the one above. If you never run any of them, click here for a first guided tour in the Mandelbrot Set. Don't worry, there will be no mathematics at all! By the way, you will also get a first contact with a basic property of the fractal pictures, the self-similarity, which we shall meet again many times in the following. A similar walk can be done across the Markus-Lyapunov pictures if you have the relevant explorer software for this kind of fractals.
In fact, it seems that these bursts of colours, so fascinating for the
layman, were a pleasant surprise for the pioneering mathematicians in
the 1970-80s. In their mind, the Mandelbrot Set was mainly the figure
on the right and they were specially analyzing the complicated structure
of its outline. Benoît Mandelbrot himself recounts this adventure in his
book The IFS fractals ("Iterated Function
Systems") also play a great part in the saga of fractals. They have been
developed by Michael Barnsley in a book with a provocative title,
Maybe the reader could feel entitled now to expect a clear, comprehensive, definition of a fractal. I shall refrain from giving any attempt. After all, one can read the whole book of Mandelbrot without coming across this definition! So do not expect any accurate statement. After the preceding examples of
curves, duly stamped "fractals" by the real scientists, we shall remain
with the somewhat vague idea of very irregular curves (or surfaces),
with a more or less obvious Also, it seems that a fractal object must be characterized with a
fractal For the "artist" –we shall discuss the label later on– there are two domains where fractals are of interest. - Various fractal tools exist, most often in commercial packages, that can simulate natural landscapes or provide various textures to be mapped on surfaces in 3-D software. Generally, the artist will emphasize the natural or realistic look of his pictures and not its fractal features, and he will not claim the "Fractal Art" label for them –barring exceptional cases which will be considered later on.
- On the opposite the supporters of this
*Fractal Art*produce non figurative images, most often highly coloured, through software with a marked flavor of applied mathematics. Typically, a number is computed for every pixel in the figure, through some algorithm more or less complicated, then this number is translated into a colour. User-friendly software exists for the most classical algorithms, such as those for the Mandebrot Set and its close relatives, that spares the user most of the mathematical details and claims a few mouse strokes only to compute the pictures –maybe also a bit of patience while computations are carried out. But there also exists more complex programs with which the user may input a mathematical function of his own, thus adding a new dimension to the artistic value of the work. It must be noticed that most of the available software is shareware or public domain. However, there also exists a few creators who write their own software completely.
The layman specially knows the pictures from the Mandelbrot Set,
and, paradoxically, he sometimes reject them because he saw too many of
them. I came across this reaction several times with image people and I explain
it with the large spreading of free software to explore the Set; too
many people tried and stopped too rapidly, obviously on nearly the same
pictures, which would have been astounding ten years before, when
By way of examples, I add a few very simple pictures, obtained some years ago with an Amiga computer, and a few far more advanced pictures, signed by some of the best specialists on the Net. The difference in quality should be undisputable –and this might awake a few more vocations... Click here to get basic information on the main available programs, together with a few useful links. Click here to get the references of the various books, articles and web links that I used to prepare these pages.
[ Return to home page ] [ Art and Fractals Contents ] - Discovering the fractal world:
- Introduction - Mandelbrot Exploration - Lyapounov Exploration - Von Koch Curves - IFS Fractals - Fractal Dimension - Mandelbrot Relatives - Finest Fractal Pictures - Software - Biblio and Links
- Fractals and mysticism:
- Introduction - The Mysticism of Infinite - Non-Euclidean Art?
- A new Art?
- Introduction - Fascination of Fractals - Fractals and Photography - Definitions of Art - The Colour Choice - Other Colour Choices - Fractalists Painters - Compositions with Mandelbrot - Put a pretty girl - Algorithmic Art - Beyond the "Fractal" Art
Charles.Rosemarie.Vassallo@wanadoo.fr |