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 Fractals, the French mathematician Benoit Mandelbrot overcame the limitations of Classic (Euclidian) Geometry to describe the complexity of 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.” [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 components.

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. The set can be seen on YouTube under Mandelbrot Set Zoom. Watch the pattern of the original shape reappear over and over as the program descends deeper and deeper into the set. It is beautiful to watch.

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

Let’s apply the Mandelbrot Set using some of the fundamental characteristics of our Universe as a Master Model (equilibrium, self-containment, self-generation, self-perpetuation, relative degree of freedom in adaptation) and start a descent into some universal components; a galaxy, a planet, a human being. As we descend into smaller spheres, we begin to see a reiteration of the fundamental characteristics … the blueprint of the Master Model … re-occurring on the components, showing that everything is fundamentally similar, and therefore, interrelated:

  •    As our Universe, our galaxy has obeyed an innate tendency to attain, and sustain, relative states of optimum equilibrium between its energy and mass contents … more mass demands more energy, less energy demands less mass. This is Einstein’s magnificent insight into the nature of reality, e=mc2, which means that no matter how large or small, simple or complex a naturally evolving system might be, its energy and mass contents must remain relatively equivalent.
  •    As our Universe, the Earth has unfolded into a self-contained, self-generating self-perpetuating system while preserving a more or less fundamental configuration.
  •    As our Universe, you and I are endowed with a relative degree of freedom to manipulate and be manipulated by the movement of Evolution.

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, and so forth … we find the reiteration of fundamental characteristics.

And because the fundamental characteristics of our Universe … the common blueprint … are reiterated in each and all of its components, including 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. Highlight mine.

Revised July 2018

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