42 – Fractal Geometry, the Mandelbrot Set and the Universal in us.

Fractal Geometry is one of the most succinct and revealing Scientific Theories of the 20th Century. With Fractal Geometry the French Mathematician Benoit Mandelbrot overcame the limitations of Classic (Euclidian) Geometry to describe the complexity of the irregular shapes in the natural world.

“A Fractal can be defined as ‘A rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole,’ a property called self-similarity.”[1]

“The most striking properties of these ‘fractal’ shapes are that their characteristic patterns are found repeatedly at descending and ascending scales, so that their parts, at any scale, are similar in shape to the whole. Mandelbrot illustrates this property of ‘self-similarity’ by breaking a piece out of a cauliflower and pointing out that, by itself, the piece looks just like a small cauliflower. He repeats this demonstration by dividing the part further, taking out another piece, which again looks like a very small cauliflower. Thus every part looks like the whole. There are many other examples of self-similarity in nature. Rocks on mountains look like small mountains; branches of lightning, or borders of clouds, repeat the same pattern again and again; coastlines divide into smaller and smaller portions, each showing similar arrangements of beaches and headlands. Photographs of a river delta, the ramifications of a tree, or the repeated branching of blood vessels may show patterns of such striking similarity that we are unable to tell which is which.”[2] But the most striking examples of self-similarity are found in the reiteration of the most fundamental characteristics of our Universe on every one of its component elements.

The Mandelbrot Set, a computer generated program named after Benoit Mandelbrot, was designed to show these repeating patterns at descending and ascending levels of magnification. To see the Set go to a search engine and look for Mandelbrot Set Zoom – You Tube. Watch the pattern of the original shape reappear over and over as the program descends deeper and deeper into the Set. It is a beautiful thing to watch (the volume can be turned off if you don’t want to listen to the song).

On Post 16 ‘Our Universe is a Hologram’ I wrote about the fact that if a Hologram is broken into pieces, each piece … no matter what size or shape … contains the information from which the whole image of the original Hologram can be re-generated: Each piece contains the information of the whole. The Mandelbrot Set is based on this same principle but from a different angle: The Whole is contained in each of its component elements.

Let’s apply the Mandelbrot Set using our Universe as the Master Model and start a descent into smaller and smaller universal components; first into its immense clusters of galaxies, then into its individual galaxies, and so forth into its solar systems, its planets, its animal species, its human beings, its cells, its molecules, its atomic particles. As we descend deeper and deeper into smaller spheres, we begin to see a set of common characteristics … a common blueprint … re-occurring in each and all of the elements, proving that we are fundamentally homogeneous and thus interrelated:

• Our Universe, as every one of its component elements, including us, is the sum total of intimately interconnected elements congregated into a relatively pre-determined yet dynamic and unique whole. How else can we explain that billions of galaxies take the common shape of a Spiral yet each is so downright unique, or that Hydrogen atoms share the same fundamental structure –a nucleus and a single electron– from one end of the Universe to the other yet each atom is a unique entity? How else can we explain that billions of human beings can each have such a unique mind … a mind like there is no other in the entire Universe … yet, like our Universe, our component elements grow into a more or less pre-determined structure?
• Our Universe, as every one of its component elements, including us, has grown from inception to its current state driven by an innate tendency to attain, and sustain, relative states of optimum equilibrium between its energy and mass contents … more mass demands more energy, more energy entails more mass. This is Einstein’s magnificent insight, E=mc2, which truly means that for any natural system … like our Universe, like our solar system, like you and me … to attain, and sustain, relative states of optimum equilibrium, its energy and mass contents must be in continuous balance. But because we have not yet learned to see our Universe as a natural and evolving system, we are still in the dark about the primordial equalizing forces that sustain its stars and galaxies and human beings in dynamic yet relatively balanced Permanence throughout our existence.
• Our Universe, as every one of its component elements, including us, has unfolded amidst utter uncertainty and infinite probability into a self-contained, self-generating and self-perpetuating System that, although constantly developing and changing, manages to preserve a more or less fundamental and foreseeable configuration. How else can we explain the fact that, like our Universe, a human lifespan remains basically the same, the same Persona, the same self-perpetuating system, even if our atomic components are constantly being replaced?
• Our Universe, as every one of its component elements, including us, is endowed with a relative degree of freedom to manipulate and be manipulated by the movement of Evolution. How else can we explain the Fact that a star like our Sun has managed to sustain a dynamic planetary system in steady orbits for billions and billions of years, so Life could explode into myriad creatures and become self-aware of itself in the form of a beautiful human animal? How else can we explain Order, or Sel-reflection, or Purpose? Just look at the DNA helix, or at the self-reflection of a baby as it learns to walk, or at the purpose of an ovum and a sperm when growing a brand new human being.

The Mandelbrot Set is a new insight into the nature of our Universe. When we zoom in repeatedly from one sphere into another … from dimension to dimension, from galaxy into solar system, from solar system into planet, from planet into human being, from human being into molecule, from molecule into atom … in the thorough interrelatedness of our component elements, in our innate tendency towards equilibrium, in the uniqueness and universality of our fundamental characteristics (self-bounding, self-generating and self-perpetuating), in our innate capacity to manipulate and be manipulated by the movement of Evolution … we find in each and all of us extraordinary repetitions of the fundamental universal design.

And because the fundamental essence of our Universe is imprinted in each one of us, the magnificent mystery can be glimpsed at by understanding ourselves.

Share the Knowledge.

[1] From Wikipedia
[2] Excerpts from The Web of Life by F. Capra. Highlights mine.

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