A fractal is an object that has the property of self similarity, ie that each of its parts is very similar to the whole and the basic structure is repeated at different scales. The term was proposed by the mathematician Benoît Mandelbrot in 1975 and derives from the Latin fractus, meaning broken or fractured.

**A fractal object has the following characteristics:**

– It is too irregular to be described in traditional geometric terms.

– It has detail at any scale of observation.

– It is self-similar, meaning that each of its parts is similar to the whole.

In nature fractal geometry also appears, as in this romanescu (hybrid of broccoli and cauliflower).

In the words of Mandelbrot himself, “Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line”.

A **natural fractal ** is an element of nature that can be described by fractal geometry as clouds, mountains, blood capillaries, respiratory trees, fern leaves, coastlines or snowflakes.

This representation is approximate, because the properties attributed to ideal or mathematical fractal objects such as infinite detail, have limits on the natural world.

Here are some more examples:

There are, then, natural and mathematical fractals.

Of the mathematical fractals, the best known and most studied is the Mandelbrot set.

It is amazing to observe its infinite complexity, which multiplies in all scales. No matter how much we increase the scale or how close we look into it, on the screen will still appear infinitely more and more complicated shapes.

All this complexity is generated by the following formula:

#### Z=Z^2+C

Its appearance, increasingly known and recognized is this:

To get an idea of its richness and complexity,

the following image is an approximation of 35 times

in the image above: