We can think that nature is ruled by chaos and chance, as if life had been created as a result of a series of coincidences that have brought us to where we are today. Without denying that this happens, within this perfect random and unpredictable chaos, we find that a certain sense of harmony still prevails when verifying that some of the creations of the Universe are organized in fractals.
But what exactly are fractals
, how are they formed?
And most importantly, are they more than just the capricious intervention of fate?

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What are fractals
In short, when we talk about fractals, we are referring to objects with a geometric shape that, inside, are in turn composed of smaller patterns that have the same shape. Reducing to smaller and smaller scales, we could see how this trend is repeated ad infinitum , although they are compressed in a limited space.
If we also observe different creations of nature, we could see how the organization in fractals is a constant that is repeated throughout several cases .

A brief history about fractals
We owe this curious term to the mathematician Benoit Mandelbrot (1924 – 2010), who coined it in the mid-1970s. It is said that this Polish-born calculation genius found the inspiration that would lead him to describe what fractals are while contemplating the coastline that outlines the silhouette of the island of Great Britain . Such was the curious mind of Mandelbrot, who set out to find out how much the entire coastline of the great insula measured.
But, how could he find the answer to such an ambitious question?
After all, geography was not formed following any established pattern, but rather is the product of millions of years of profiling, caused by the main eroding agents and, to a lesser extent, measure, by the action of man. So, did his riddle have an answer?
I had it. Although it may sound obvious, the theorist realized that, if he used units of measurement that were smaller and smaller, the length of the coastline increased, although it always remained the same. Curious paradox, is it not so?
Mandelbrot deduced from his experience that there could be objects of geometric shape not yet defined by mathematics , objects that he would nickname “fractals”.

The 3 most characteristic features of fractals
Due to their nature, there are a number of characteristics that help define what fractals are.

1. Dimension in irrational numbers
Contrary to other elements with beginning and end, fractalsthey have a dimension that can only be expressed by irrational numbers , because they never end.

2. Fractals have no end
If we reduce the distance at which we focus on a fractal at smaller scales, we will see that these patterns stretch to infinity, increasing their length .

3. They follow patterns
No matter how close we get, fractals follow the same pattern repeated countless times even on millimeter scales . So much so, that the appearance of many fractals that make up a larger object actually have an almost identical appearance to this larger whole.

10 examples of fractals in nature
There are many elements whose structure is in the form of fractals in nature itself or in everyday life, although it is true that we would need a magnifying glass or a microscope to be able to perceive their appearance.

1. Art
Fractals can also manifest themselves in different artistic expressions, so much so that there are already those who speak of “fractal art”, which can be created through computer programs that allow these figures to be made that combine science with art; two disciplines that no one would have ever said could go hand in hand.

2. Trees and plants

The structure of the flora is also organized in fractals. From a more macro level (the trunk of the trees branches into smaller structures, the branches, from which leaves sprout), to a more micro level (the nerves of the leaves are branched extensions that constitute said sheets).

3. Romanesco broccoli It
may be an unappetizing dish, but this kind of cabbage represents an example of a harmonized fractal, with a beautiful design in almost perfect spirals that twist and rise from the base of the broccoli stalk .

4. Corals
These colonies of organisms that live attached to the rocks of the seabed are also organized in calcareous formations with a branched appearance and beautiful colors .

5. Cancers and tumors
Even these bulging masses of cells are structured in fractals. Apparently, it can be recognized whether they are benign or malignant tumors based on their silhouette : those that are not harmful are more rounded, while the fractals of harmful tumors are more stylized and amorphous.
This knowledge would allow great advances in biology, since it would thus be possible to determine the extension of the entire fractal and whether it would spread throughout the body making metastases.

6. Music
Although it is not perceptible to the naked eye unless we have a printed score, the musical melody is also composed of ascending, descending or alternating fractals and with a tendency to repeat within the same theme.

7. The plumage of some birds
For example, the great tail of the iconic male peacock, which, when unfolded to attract females, forms a beautiful pattern in the form of fractals that recall hundreds of eyes. Likewise, the wings of many butterflies and moths simulate two large eyes like a bird of prey to warn possible predators.

8. Lightning
The electrical discharges that take place during storms are not lightning that falls at perfect angles, rather the opposite, they are a perfect example that fractals in nature are something very present . Even clouds can be considered types of fluffy fractals.

9. Rivers
Another very clear example of fractals in nature can be found in the way riverbeds look from a bird’s eye view or on a map. In some cases, the path of these water currents, from their descent from the mountains , forks into tributaries and channels smaller than the main artery, which runs to the sea.

10. Circulatory system
If we observe the intricate network of blood vessels and nerves found inside our body, we will see that these ramifications exist just like in the trunks of many trees or in the veins of the same leaves of these large plants.

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