Fractals: art of mathematics

2002/06/27 Elhuyar Zientzia

• Matematika

You can paint the canvas with acrylic, pastel or oil to create a beautiful picture. We can use the most striking effects of the camera to make a good image. But the structures that nature has known since time immemorial also create beautiful images. These are fractal structures.

The fractal is a mathematical object whose form always follows a repetitive model, that is, the fractal is similar to itself on different scales. Therefore, it does not matter how many times we expand the image, since we will always have quite small details.

In nature there are many examples of fractals: for example, it can be treated mathematically through systems of fractal branches of a tree, since, in short, the repetitions of a simple design (union of the two branches) give rise to a very complex system (the whole tree). Each smaller branch also has the appearance of the main branch and, elsewhere, both can be treated the same way. Although we look at a grain of sand with a good magnifying glass, it seems to us that it is a rocky lump, and the pulmonary alveoli or arteries of the heart clearly show the pattern that reproduces at different scales.