Hunting for the hidden dimension: fractals

Hunting for the hidden dimension: fractals

Many shapes in nature can be described by using fractals. You can recognize a fractal when a pattern is repeated many times. Endless repetition is the key to fractals, by repeating the same shape over and over again. Fractal geometry is a way of looking at things. Once you realize it exists you begin to see it everywhere. It’s a way of perceiving the world that leads us to developing new inventions. Nature has always been shaped as fractals; it was discovered as a mathematical equation.

“Think not of what you see, but what took to produce what you see” The whole of a fractal looks like a part, which looks just like a smaller part. This geometric concept is a way of seeing how we are all one. We are all made of the same material. There is something we have in common with the world that surrounds us. We don´t live in it, we are part of it. Fractals can prove how every tiny part of a whole looks and acts like the whole itself.

Classic mathematics only work to measure the world we have built, using regular shapes: straight lines, flat surfaces, circles, triangles. Nature could not fit into these regular shapes. For clouds, leaves, mountains there is a way to use mathematics and formulas. It is just a different way of thinking. Benoit Mandelbrot is a mathematician that stood outside the mainstream. He was interested in the point where mathematics and the eye join, he could see formulas transformed into shapes. After he got his Phd he joined IBM a company that was looking for people like Mandelbrot who knew they could do more with the world. In IBM people worked with monsters that were irregular shapes in nature that had a pattern which repeated itself over and over again every time in a smaller version of itself. Mandelbrot could see this same pattern in sound. He saw how the same wave of sound repeated itself in the same shape for an hour, minute and second.

Lewis Fried Richardson discovered that we cannot measure coast lines because they have fractal-like shapes. This means they are infinite. The length of a coast line depends on the measurement method we use to measure, even though we cannot measure the exact length of a coast line.Every set in mathematics can go on forever. It is almost impossible for humans to see a complete set. At IBM, Mandelbrot could run an equation millions of times using a computer, something that went way beyond the Julia set which was discovered in the early 1900´s.

With the computer Mandelbrot developed a shape that could represent fractals. It is known as the Mandelbrot set which is a mathematical set of points whose boundary is a set of two dimensional fractals.  If you zoom the Mandelbrot set you can see how the same structure repeats itself without  limit.

After Mandelbroit’s discovery, fractals were used in different areas. For example, Jhane Barne started using fractals when designing clothes. Willi Geiger fractals for special effects and Nathan Cohen in cables, he realized that by making antennas smaller they will be  able to receive more frequencies. Now you can see fractals in cell phones and other communication devices. Fractals were also used to solve the mystery between mass and energy consumption. A group of biologists were able to measure how the forest as a whole takes CO2 by measuring one single tree with fractals. Fractal geometry gives us a new language to read nature. Now we can read nature and translate it into mathematics formulas.

How can we apply fractals into yoga practice?

“Once you see it, you cannot stop seeing it” This same principle applies to fractals. Fractals are a way of perceiving nature. Once you know they exist, you begin to see them everywhere. This same principle applies to yoga. Everything I have learned through my yoga practice is related to concepts of life and humanity that have always existed but we cannot see them until we experience it. Once you meditate and feel your inner self, you cannot stop feeling or stop being conscious of that self.

Repetition: doing the same over and over again. Yoga is a practice and the only way to improve your practice is by repetition. Nowadays repeating can be seen as boring and old. However, repetition is the only way we can get good results. The interesting part is that is an endless repetition where we cannot search for results, just enjoy the process.

 

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