arrWhat is a fractal
arrAre fractals only mathematical objects?

What is a fractal?

It is a good question! In simple words, they are pictures which have similar characteristics at different magnifications.

They are not simple graphics but are based on mathematical functions. These functions give complex geometric shapes. Their main characteristics are:

  • complex structure at any level of magnification;
  • a non-integer dimension (I know that is not simple to believe). Instead of lines (dimension equals to 1) or surface (dimension equals to 2), the dimension of a fractal is by example 1.342;
  • they have a perimeter of infinite length but an area limited;
  • they are self-similar and independent of scale. In other words, each small portion of a fractal, when magnified, can reproduce exactly a larger portion.

Well, I hope that you are not too discouraged. It's not necessary to understand the mathematics under fractals to appreciate them.

Are fractals only mathematical objects?

Not at all!  Fractals are everywhere.
The shapes of leaves, trees, clouds or rivers are all fractals. Fractals are the rule and not the exception in the nature.

Copyright 1997-2024 Philippe Wautelet