Definitions of Fractals

Generally spoken, so-called “fractal” objects are objects that reproduce themselves on a more or less large scale, and this infinitely. These objects can be obtained from simple elements, through curves or sets of dots.

There are various definitions of fractals. Some of these definitions are complicated fractal mathematics and some are definitions for non-experts like me. Therefore, I will be able to give you only an explanation of self-taught basic fractal geometry since I started creating fractals in late 1999.

There are two main features to fractals. One feature is all fractals exhibit self-similarity at all scales. This self-similarity may be strict or loose. Strict fractal self-similarity is rare in nature and may be non-existent.

Let me try and explain loose self-similarity a little further. Imagine you’re in the kitchen and prepare a whole cauliflower for dinner. So what do you do? First, you break off a big branch from the whole cauliflower. What do you see now? You see a small cauliflower which looks similar i.e. loosely self-similar to the whole cauliflower you had a moment ago.

Now if you were to continue breaking off even smaller branches of cauliflower you’d end up with ever-smaller replicas of the whole cauliflower until nothing was left. That in effect is what fractals are, self-similar replicas at all scales. I know this is not how you prepare cauliflower but I hope you’re able to understand the nature of fractals a little more.

The other main feature of fractals is that they have infinite detail, though not always.
There are eight pictures galleries currently here. And each gallery contains 12 fractal pictures. All the fractals have been created with Ultra Fractal. Also, all the pictures are available as fractal posters.

Some people think fractals are trippy pictures. Some people think fractals are weird pictures. And some people even think fractals are funny pictures. I, however, believe most fractals are Priceless Pictures! See what you make of them and I’m sure you’ll agree.

The word Fractal was first used in 1974 by Benoît Mandelbrot in 1974 and is derived from the Latin root fractus meaning broken. Fractal was originally an adjective like in “fractal objects”.

To give you a visual ides, let’s look at a square. If you would add on each side a side square that is twice as small on the right on each side in the example. So we add 4 squares added in total.
Then, on each of these squares, we apply the same formula (now there are only 3 additional squares, the 4th being on the initial square). So we have 3×4 or 12 squares more!
And so we go on, and on, and on…

The object “iterated” an infinite number of times is contained in a space that is indeed finished. The surface therefore necessarily tends towards a finite number.

Fractals are the computer graphical representations of complex sets. The study of these sets is a  branch of fractal geometry. The art and the name Fractal was born thanks to the intuitions and work of mathematician Benoit Mandelbrot. It is to the credit of Mandelbrot to have disseminated the study and representation of these sets on a global scale.

The main characteristics of fractal sets are the extremely irregular and chaotic nature of the contours and the self-similarity. Their form is recurrent in any place and at any scale. Only thanks to the computing ability of modern computers can you observe and understand these characteristics.