Fractals: a mathematical delight of existence

It seems that the human mind is meant to look for patterns in chaos and is so adept that it has the ability to find faces wherever it sets its mind, an effect that has its own name. And it is that strangely the patterns generate a feeling of well-being, a kind of mental stillness invades us when we observe the most intricate patterns that we know as fractals. But why does this happen? Science answers.

What are fractals?

There are structures that are so strangely perfect that they hide mathematical patterns, as discovered in 1975 by the French Benoit Mandelbrot, who was in charge of giving them the name of 'fractals'. Since then, the charm of fractals has invaded the collective imagination and admiring them could certainly be said to be close to meditation.
Technically, fractals are geometric shapes that can be spatial or flat, that are self-similar or self-referential and that have the peculiarity of being projected in different magnitudes without losing the same patterns of the original shape. That is, no matter how close or far away it is, the fractal composition always retains its patterns.


Similar to listening to Bach music

Richard Taylor, who is a physicist at the University of Oregon, was captivated by the effects that fractals generate in the mind after observing Jackson Pollock's paintings. From his perspective, the work of the abstract expressionist artist kept within it a series of fractal structures. Since then he has been studying how these intricate patterns impact the brain. To find out, he conducted an experiment in which he connected probes to measure brain activity in different participants while they were exposed to images of nature transformed into fractals. Taylor found that the volunteers preferred images on a scale between 1.3 and 1.5 of the mathematical dimension levels D, which is a scale for assessing the complexity of fractals.

He also observed that exposure to such images was highly correlated with alpha-wave brain activity in the frontal lobes. These waves present in these regions of the brain occur when the subject experiences a bridge between pleasure and relaxation. It is for this reason that Taylor and his team concluded that observing fractals has a similar effect to listening to music by Bach or Brahms.

In this sense, when we admire the fern leaves or the ocean coastline with its large fractal branches, we are experiencing a sensation so relaxing and pleasant that it is close to listening to music.

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