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.

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 and is derived from the Latin root fractus meaning broken. Fractal was originally an adjective like in “fractal objects”.

To give you a visual idea, 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.