The Mandelbrot Set

The Mandelbrot Set is amazing, both by itself and by what it explains

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11. The Mandelbrot Set

— A Marshmallow Man made from many Marshmallow Men —

Benoit Mandelbrot

Benoit Mandelbrot
Benoit Mandelbrot

Another Chaos pioneer, and probably the most celebrated one, was Benoit Mandelbrot as his famous Mandelbrot Set has served as symbol of Chaos Theory ever since the field emerged.

The Mandelbrot Set is a graphic image, just like the rain-or-sunshine graph of Lorentz, except that the Mandelbrot Set doesn't really cover some real process. It's just a formula that gives a pretty picture (endearingly nick-named the marshmallow man), but there's something very special about this particular picture because when we zoom in on any part of it, we are bound to come across the very same basic form, embedded in the texture of the mother image.

But the little marshmallow man is not an exact duplicate of the mother image. It obviously follows the same basic design but is always unique. Not unlike snow flakes.

If we would then zoom in on that little marshmallow man, we would find more swirls and eddies and deep down again a marshmallow man! The Mandelbrot Set contains infinite detail, and infinite layers upon layers of marshmallow men embedded in terrific swipes of frozen motion:

Mandelbrot Set

Take your time to admire the Mandelbrot Set. It will help you understand the Universe...

We recognize the marshmallow man in the first and last frame and make a connection, but the large-scale marshmallow man contains not only the little ones, also all those sea-horse tails and swirls and eddies. Then all those swirls must be part of the little marshmallow man as much as they are part of the big one. It's not just the little, recognizable image of the marshmallow man that constitutes an element of the larger whole, but a tornado of motion of which the marshmallow man is only the eye.

Imagine we're taking an elevator down the abstract space of the Mandelbrot Set. We start off on the top floor and start sinking down into the splendid expanse wafting out as details emerge. We pass loosely connected clouds of blue dust, firmly connected 'objects' and finally a replica of the top floor but slightly different; we have reached what we will call the first floor down from top. Sinking further down into the swirls and eddies of the first floor down we will pass more clouds and shapes, and after a while again a replica of the first floor down. The Mandelbrot Set is truly a magical place.

Marshmallow Man top floorConsists of
Mandelbrot Set Loosely related smears

Tightly knitted forms

Marshmallow Man 1 floor down

Marshmallow Man 1 floor down

Consists of
Mandelbrot Set Loosely related smears

Tightly knitted forms

Marshmallow Man 2nd floor down

Marshmallow Man 2nd floor down

...etcetera

In chapter 8 we have already established that the math upon which the Mandelbrot Set is founded does not take in account quantum fuzziness because math can not duplicate pure randomness (which means pure unpredictability and the quantum sovereignty upon which the universe is founded). So, let's imagine that we do take in account quantum fuzziness. Let's imagine that the little marshmallow man (and all its protruding eddies) is a quantum, and the large marshmallow man is the structure that the quanta form.

Now imagine that the little marshmallow men are atoms and the big one is a large structure (like a snow flake). Those eddies then become a fine representation of the atoms' force fields and behavior; the webs of energy that binds them all together to form the big one.

Or imagine that the little marshmallow men are bees that together make a hugely complex hive. Is that right? Does the marshmallow man story apply to a bee hive? Why doesn't a beehive look like a big bee?

Well, it does! The little bee is not just the motionless image of a bee but its entire behavior, its instincts and function in the hive; the swirls and eddies of the little marshmallow man. And not all little marshmallow men of a beehive are the same; there are different ones. And together they make a structure that comes from the inputs of all those little different little ones. The hive comes from bees and from nothing else.

Same goes for ants that make an ant hill. Same goes for humans that make a planet buzz with cities and governments and satellites in orbit.

Surprised that a principle based on quantum fuzziness is applicable to animals and humans? Then hold on to your cortical node because it is about to blow.

Go to the next chapter:
The Household Set

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