Fractal
From Ultrafractal Wiki
A "fractal" is a mathematical object defined by a formula, that has a number of interesting properties, self-similarity and complexity.
Images of fractals can of course be created using UltraFractal, though not every formula generates a fractal, indeed, some formulae (such as Julia) produce a non-strictly-fractal object (ie a circle) for certain settings.
There are also plenty of examples that give a fractal only in a very trivial sense (for example: the "droste" effect, its UF implementation is here).
Contents |
Self Similarity
One of the most important things that makes an object fractal is a quality known as self-similarity.
This property implies that an object resembles itself somehow across different scale levels. This similarity needn't be exact however, it may be another sort of quality that is preserved, rather than exact shapes and details. A good example of non-exact self-similarity is a cloud, in which the quality that persists through scale levels is the "distribution of sizes of details" (or "frequency spectrum"), rather than the actual specific shapes.
Self-similarity alone is not sufficient to properly describe what a fractal is however because even a simple line or a circle have this property. Fractals also need "Complexity".
See also: Wikipedia on Self-Similarity.
What are Fractals? Question from Robert
I often get confused looks on faces when I try to explain fractal art and how I make my renders.
I'm going to a new exhibition in Malmö, Sweden next month and would like to be a little prepared.
Is there a formal definition of fractals and the artform? In its simplicity so non mathematicians can understand the concept.
I'm putting a small sign at my exhibition this time!
Robert
Ron's Reply
Hi Robert,
Using a bit of artistic license I would say (and do say) fractals are mathematical objects, but they are also objects of nature, as in the branches of a tree, the structure of a leaf, the image of a cloud, the terrain of a mountain and the shape of a coastline.
Ron Barnett
Kerry's Reply
Since fractals are mathematical objects, any formal definition would be mathematical and thus, probably not well understood by the general public.
However, a simple description is possible--I say that fractals are shapes, conceptually similar to familiar shapes like squares or circles. However, they are also shapes that have detail at all scales. That is, when you magnify a piece of a square or a circle, it will eventually become indistinguishable from a straight line, because those shapes are smooth.
Fractals never smooth out--no matter how much you zoom in, they are still rough.
That's the easy part. :-) A definition of "fractal art" is tougher, but I think you'll be safe to say that it's an art form that features fractals significantly. When in doubt, just show pictures. :-)
Kerry
External Links
- See 'What are Fractals?' in UF5 help
- Also Wikipedia on "Fractal"
- Damien Jones explains Fractals for the layman
