How does the Universe impose its fractal-like patterns of order on chaotic systems? (Strange Universe series)

Complexity can come out of simplicity and a simple equation can generate an infinitely complex pattern eg The Mandelbrot Set Time and repetition can generate complexity from the simplest of beginnings.

I don’t know.

But I would like to emphasize something important about chaos (and by extension, fractals). Chaos, philosophically, is actually really profound and amazing.

A lot of people think chaos just means “randomness” or “unpredictability.” Chaos is random, but that’s not what’s important about it. The “point” of chaos is that it is randomness that emerges naturally from a non-random, deterministic system.

For example, there is a basic, deterministic and simple equation for population growth (such as a population of rabbits over time). This equation, if you iterate it enough, starts outputting numbers that fluctuate like a wave between two points. Then it doubles to four points. Then it doubles again to eight points, and sixteen, and so on… and then, eventually, it becomes completely random. It’s “chaotic” because after a certain amount of time, completely random behavior emerges from completely deterministic behavior.

I think this concept is related to fractals and the Universe’s simultaneous order and diversity. A fractal is self-similar, it’s deterministic in the sense that it can be described by a simple equation and clearly has a lot of order… but at the same time it is infinitely variable.

Here is an example of the above that I have had a lot of fun with.

The oddest case of chaos in a determinist system to my mind are the prime numbers.Nothing could be more deterministic than the sequence of the natural numbers 1, 2, 3….. and yet the distribution of the prime numbers within this sequence seems completely unpredictable. Despite this we can approximate how many primes will be in a given range of numbers and so chaos and predictability exist side by side and are not mutually exclusive.

@flutherother Exactly. What truly amazes me is that in a chemical reaction like the BZ reaction shown in third video link of the question’s details,billions of molecules of various chemicals are combined and start to organize in very clearly visible patterns, as if molecules separated by many thousands of times their own girth know exactly what all the other molecules are doing. We see some sort of that in all nature’s self-similar patterns—and they are truly just about everywhere we look in nature. Can you even conceive of the super computer it would require to calculate all of those patterns everywhere in the Universe simultaneously? Nature can, and does. PS: The tool in your second comment is utterly fascinating. When you add a third very low-mass body, the motion can become amazing.

@Qingu I am as deeply in awe of it all as you. Thanks.