Mandelbrot Set Explanation

Life is wonderful and it is complex. So complex even that we have no idea how it came about, nor do we have a universally agreed upon definition for it. What we observe however is that life has something to do with complexity. We're not sure if a virus, an inanimate package of "dormant" genetic information, is to be regarded as life; there's no sharp boundary to point out (yet) where inanimate and lifeless matter is interconnected in such a way that it becomes life.

_{source: Wikipedia}

The same is true for consciousness; we have no idea how it comes about, but here too our observations suggest that it has a correlation with complexity; more complex nervous systems seem to translate into more consciousness, for lack of a better way to put it. Worm brains with a couple of hundreds or thousands of loosely interconnected nerves, are no match for a mammal's brain that contains billions upon billions of tightly interconnected nerves; and the human brain is still the most complex system ever discovered in the universe.

How does this all relate to the Mandelbrot set, you might ask. You might even wonder what the Mandelbrot set is. I believe most of you have seen it, or at least the wonderful graphical representation of it, of which there are many online; I'll link one of the many zoom videos below this paragraph, and it's one that has a short explanation of what the numbers in the Mandelbrot set are. The formal description is a bit too hard on my brain: "The Mandelbrot set is the set of complex numbers for which the function does not diverge when iterated from, i.e., for which the sequence, etc., remains bounded in absolute value." The video is only for minutes in total; please watch it before continuing:

_{The Mandelbrot Set: How it Works, and Why it's Amazing!}

The graphical landscape of the Mandelbrot set is infinitely complex, yet arises from a relatively simple mathematical equation which is iterated over and over again; the endless iteration of simple rules creates infinite beauty. And this seems to be a re-occurring phenomenon in nature. Living things are made up of the same stuff we use to build inanimate things. We can see and measure every chemical component, every reaction and every electrical signal that comprises a living thing, but we're utterly unable to reconstruct a living thing from scratch. I love the anime series Fullmetal Alchemist, which illustrates this perfectly; the protagonists, two brothers of which one dies in a forbidden experiment to bring back to life their deceased mother, must gather all the "ingredients" used in the "recipe" to make a living human body:

The physical body, which is a complex system of bones, muscles, organs, nerves and blood vessels developed for optimal interaction with the environment, follows standard natural laws and patterns that, while different between species, are similar to all animal life on the planet. It has been stated that, broken down to its barest components, the average adult human body is comprised of Water (35 L), Carbon (20 kg), Ammonia (4 L), Lime (1.5 kg), Phosphorous (800 g), Salt (250 g), Saltpeter (100 g), Sulfur (80 g), Fluorine (7.5 g), Iron (5 g), Silicon (3 g) and fifteen traces of other elements.
_{source: Fullmetal Alchemist Wiki}

These are only the ingredients needed for the physical body, and the brothers fail because they screwed up the most important ingredient for a living human, which is the soul or the spirit. But to stay with just the body for a minute, it's clear that not the basic ingredients themselves, but the complex interactions between the individual molecules and atoms that make up the ingredients, are responsible for the emergence of what we call "life." What the Mandelbrot set proves, as well as many, many other things and observations, is that all this wondrous and beautiful complexity can arise from the execution of very simple rules between very simple basic components, given enough time to re-iterate ad infinitum.

I like to always consider the other side too; if life and consciousness are the result of increasing complexity, of more complexity is needed to sustain higher consciousness, could the reverse be true as well? Should we be looking for that sharp distinction between life and non-life, or conscious and not conscious at all? If a worm is just a little bit conscious, is a single celled organism then even less conscious, but still conscious? And the virus? Could that be just almost unconscious? And what about an even more simple entity, like a rock? Is a rock simply one of the most lifeless objects in a universe that's always been alive?

I like questions much more than answers really :-) So let me close by giving you the final part of the best Mandelbrot explanation ever; it's another short video that, together with the first one linked above, gives a solid and visual explanation why the complex numbers in the Mandelbrot set are special, but nu more special than in any other so called Julia set, and how they relate. Their shapes, how similar shapes evolve slightly on the one hand, and how they connect to completely different shapes and colors are almost life-like; the whole thing has a very "organic" feel to it, yet it springs from one very simple equation. Could this be a beginning to find the deepest secrets of life, the universe and everything else? Or is the answer 42 after all..?

_{What's so special about the Mandelbrot Set? - Numberphile}

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