Fractals are beautiful and hypnotizing. You can find them almost anywhere, in nature, culture, computers, space, and in your own body. But what are they? Most of you will have seen one already in a peace of broccoli or artwork. Strange forms, vivid colors and endlessly complex. Amazingly, fractals are simple to make.
A fractal is a natural phenomenon or a mathematical pattern that is self-replicating or self-similar. It is a never-ending pattern. Fractals are infinitely complex patterns that are self-similar across different scales. They are created by repeating a simple process over and over in an ongoing feedback loop. Driven by recursion, fractals are images of dynamic systems – the pictures of Chaos and order. And they can give us clues to the self-organizing force of nature.
Fractals are found all over nature, spanning a huge range of scales. We find the same patterns again and again, from the tiny branching of our blood vessels and neurons to the branching of trees, lightning bolts, and river networks. You may remember looking closely at the leaves of a tree, and at the branching of its veins. A fractal is a picture that tells the story of the process that created it, and maybe the story of creation itself.
The discovery of fractals is relatively new, and the understanding of fractals even newer still. Gottfried Leibniz coin the term fractal in the 17th century, but the mathematics behind it was said to be to chaotic and deemed unimportant. It didn’t become popular until the advent of computers in the 1960s, when Beonit Mandelbrot a French mathematician began using it.
The direct pragmatic use of fractals can be found everywhere; nature has used fractal designs for at least hundreds of
millions of years. Only recently have human engineers begun copying natural fractals for inspiration to build successful devices. A computer chip cooling circuit etched in a fractal branching pattern. Fractal antennas in cellphones and other devices. Because of their fractal shapes, these antennas can be very compact while receiving radio signals across a wide range of frequencies. Computer graphics emulating nature in movies or videogames. In the measurement of coastlines or rivers. Understanding hurricanes and their field of effect. The turbulent swirling of fluids and in the pattern of star formation in galaxies. Even our DNA can be understood in the terms of fractals.
Fractals are not only found in nature, but in human culture as well. Especially in African culture the use of fractals have been important. They use it braiding of their hair, art, constructing wind walls, religious symbols, and even structure their cities around the ratios of fractals. The fractals are important both in their practical lives as well as their spiritual. We can only wonder at the origin of this practice. How far back in time have they use fractals both consciously and unconsciously.
The hidden meaning
Fractal is Latin and means “to break” much like the word fracture. To break down, to split up, differentiating. To fractalize is to create something new from what you already have by going deeper. In this sense fractals are a clue to the holistic nature of the universe. The whole is greater than the sum of its parts. 1+1 becomes 3. Like a couple having a baby and becoming something more than just people living together, they become a family. They take a part of themselves to create something new. You may be a small part in all that is happening around you, but your part is important, you are a color of a much larger design. And with each other working together we become something more than just animals or humans, we become a humanity.
Everything can be broken down in parts. All the parts make up a whole, a unity, and every part contains a blueprint of the whole. The parts of a whole are in intimate interconnection, such that they cannot exist independently of the whole, or cannot be understood without reference to the whole, which is thus regarded as greater than the sum of its parts. This is the main idea of the holistic philosophy. And it has become a popular concept in many fields, from industry, medicine, to psychology, organization and education. This holarchy is beautifully represented in fractals.
A phrase comes from the beginning of the Emerald Tablet which was inscribed upon the tablet in cryptic wording by Hermes Trismegistus and is said to contain the secret to magic and the nature of the universe. “As above so below, as within so without”. The meaning of these words have been discused by the spiritualy enclined for centuries, and has many interpretations, but it seems very apt when talking about fractals. Everything you see and experience can be represented on a higher level and on a lower. This this nicely into the concepts of holarchy and fractals. Since the fractals continues endlessly higher or deeper, we can experience the boundlessness of the universe, or at least get a glimpse of it. Teachings that expressed these instructions claimed it was impossible to study the universe without studying man, and conversely that it was impossible to study man without studying the universe. To look up and out is to look within.
We have nature in our DNA, we came from nature. Every natural form is latent within us: originates in the soul whose essence is eternity. Man is a micro-cosmos and as such, contains internally all the principles of the worlds above and below himself. Although the idea that the universe and man is a series of Russian nesting dolls is disconcerting but it does have a certain appeal. Within each person is a universe of its own.
For anybody who is engaged in of self-realization or any spiritual practice, it is important to remember that anything we meet or experience in the world is a reflection of the inner world. We pull event towards us like gravity, and we color it with our psyche. Your world view defines how you experience any situation, and understanding that gives you power but also responsibility. There’s is a lot of research about how your state of mind affects the situation. Whether you are a spiritual person or not there is no denying the power of the mind, for self-delusion or self-illumination.