Part 2: The Unbearable Lightness of Fractal Being…

“Necessity, weight and value are three concepts inextricably bound; only necessity is heavy and only what is heavy has value.”

Milan Kundera -The Unbearable Lightness of Being

“Her drama was a drama not of heaviness but of lightness. What fell to her lot was not the burden but the unbearable lightness of being.”

Milan KunderaMilan Kundera -The Unbearable Lightness of BeingMilan Kundera

We live in such a complex nature that we cannot begin to imagine that existence is built upon a very simple principle. Simplicity appears to us valueless*. We want complexity.

Now I will talk about the indispensable “light but invaluable” structure of fractal geometry that exists in our lives. Fear not—I won’t be explaining geometry. I will attempt to present you a glimpse of the unbearable lightness of fractal geometry.

I’m sure you have come across those shapes which reiterate themselves continuously to infinity, like the ones below:

Imagine a simple shape such as the equilateral triangle above but a little bit different. Let your imaginative shape be built by smaller reiterations of the original shape—meaning, the copy of the shape will be added to the shape itself with a pattern, such that you will then encounter a much greater but the same structure being built upon the first shape.

Since a mere simple equilateral triangle is capable of generating shapes such as the ones above with such complexity, more complex shapes are capable of generating variations that are able to create incredibly pretty or ugly shapes with infinite iterations. It is possible to see these traces in living or inanimate all beings in our environment.

Now let us give some examples from nature.

Everything in nature, living or inanimate, plant or animal, snowflake or crystal, everything comes into being by the infinitely many iterations of atoms and cells. The macroscopic design of the entity is pretty much the same of the design at the microscopic level.

A Single Change Changes Everything…

A shape is chosen, then with its same structure a formula (function) is being written, angle of rotation and number of iterations are being determined. Hence it acquires a self-repeating pattern.

On top of all that, when a similar shape is being repeated 41 million times based on a formula… and when color changes are added to the formula…

Below you’re looking at 3 fractals with the same function and the same starting shape. I want to point out how ordinary and formless the initial shape is. The only difference among these three examples is that the angular rotation value varies among all three of these examples. Even just a single degree of a difference in the angle of rotation makes such a huge difference!

30 degree angle. It is a miracle that a regular and flowery shape comes out of such a formless and asymmetrical shape.

29 degree angle. The rotation angle has changed by only one degree but instead of a flower now we have something that’s almost like a necklace of flowers. The change caused by a single degree of difference is astounding…

3 degrees…

Let’s try another fractal example. Let’s choose another similar simply branched line and iterate it 6,464,640 times… How is this any different than the branch of a tree with leaves?

Benoit Mandelbrot is the first mathematician to bring the fractal geometry into the computational setting. He has tried the formula shown above. And although the function is fairly simple, it contains a wide scope of mathematical sub-Venn schemes, negative and complex numbers while in principle it is the same as the ones above. A mere self-reiteration.

You might have noticed that even though the same formula is being repeated in each iteration, the sub-shapes keep changing and resembling things like seahorse, spirals, and so on—but they all eventually can be traced back to the same initial shape.

Fractal geometry exists in the essence of every being whether living or inanimate. Everything in nature is a fractal function. The shape at the beginning, according to the iteration number “n”, can turn into infinitesimal different shapes in infinitely unique iterations.

“Necessity, weight and value are three concepts inextricably bound; only necessity is heavy and only what is heavy has value.”

Kundera, in his book “The Unbearable Lightness of Being”, begins with Nietzsche’s “eternal return” phenomenon. Everything that exists in nature repeat themselves over time, moving in circles, going back to their points of origin. Every cycle of repetition contains something of the previous state within its core. Kundera, finally, predicts that our being which is fundamentally a result of our cumulative experiences and is therefore heavy will break free of its weight and become unbearably light once it lets go of its bonds, taboos and relations.

Even though a simple geometrical shape is “light” or, going by Milan Kundera’s definition—of no value, when it repeats itself countless times, it becomes heavy. What is heavy is valuable, functional. Yet in the core of everything that we perceive as heavy, valuable and useful exists an unbearable lightness.

Continue Reading…

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