The Natural World Behaves Like A Fractal But Is It A Fractal?

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Offline Tas_mania

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« on: August 05, 2019, 12:07:11 PM »
When I look at nature it works on rules such as natural selection and survival of the fittest and iterates way down to the sub-atomic level a bit like a fractal. When I look at human issues such as democracy, elections and dictatorships, they seem to behave like fractals also.

Is it helpful to think of the World as a fractal or am I over-simplifying life itself?
:thumbs_up_by_craig_m:


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Offline Fraktalist

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« Reply #1 on: August 07, 2019, 01:18:37 AM »
100% yes. And no you are not simplifying it too much.
Once you add fractals into the big picture, so many open endings fall into place and start to make sense.
I could start writing pages here now, but:
I'm working on 2 talks, each 1h30 I will give at a music festical in a few weeks.
Especially the second talk on "fractal evolution" shows that evultion indeed behaves exactly like escape time fractals. And for me it doesn't start with life but with the big bang. and it doesn't end with our technology, getting rid of natural selection for modern humans, but seeing technology as the next level of complexity, the evolution of evolution.

The talks are the first time I put my 6 years of manic research into a proper structure, the first time I feel confident enough to be able to answer any question that comes back.

I'll record them and post them here for sure.

short answer to "is nature/cosmos really a fractal?"
well the only argument against it being fractal, while still showing fractal patterns everywhere is:
"Fractals are mathematical objects and are infinite. The natural world is not infinite. A fern leaf is only self similar over 3 orders of magnitude, then the rules break down. So it's not infinite, thus not fractal."
But to me this is an absolutely stupid argument. you could also say there are no perfect circles/striaght lines... anywhere in our reality, so euclidean math is only a theory.
« Last Edit: August 07, 2019, 01:29:08 AM by Fraktalist »

Offline Tas_mania

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« Reply #2 on: August 08, 2019, 12:06:34 PM »
Thanks for the reply fractalist.
If fractals expose an underlying mathematical harmony in the universe, that knowledge could be quite beneficial to anybody that accepted that 'fact'.

Example. We live in a world where better communications brings ever more problems and issues into focus. A lot of people cannot handle the magnitude of these issues. Problems like injustice, ecological damage, climate damage, overpopulation, starvation and obesity...the list goes on.
If you know the 'universal fractal' will simply iterate to the next step, then there is not much point trying to change that inevitable next step.

Possibly fractals have been a solution in search of a problem, but the problem appears to be humans and how they interact with the world. Maybe fractals can help humans mentally and spiritually?

Offline Nintendokater

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« Reply #3 on: August 13, 2019, 10:59:37 PM »
Well, I think that the dimensions of fractal are not imaginable for human mind and I can also think that it is not comparable to our world what we know right know. In the (sub)atomic scale we have relations and probabilities of positions and speed of subatomic particles and this small area is very theoretical (Planck length, Calabi Yau Manifold, quantum foam, etc.). Our observable universe contains powers from about 10^-36 m to about 10^24 Meters. Fractal zooms reach powers of 100 or more and are definitely defined by a set or iterative formula. Natural phenomena can of course be orientated at fractals, but I think that it is to soon to get a proper answer to this question, although it is a good philosophical one. Maths is a language than can express ideal units, sets, etc. and has to be converted to our world, because Maths is quite theoretical like fractals are. The possibilities of fractal visualization have not to be underestimated. But computers are quite weak with rendering fractals, especially on 3D based fractals. Fractal geometry is compared to other Math subcategories a very new one and 3D fractals came up about 10 years ago. I think, the important question is, if the construction of integer dimension (2D, 3D) stays the main workspace (Euklid dimensions) or the fractal dimension. This decision will affect our understanding of the world and what we see around us. Is a cube a simple 3D body or a very simple fractal with a simple self-similarity? The thoughts about this topic can change quite quickly, it is worth to discuss it in the next 10 or 20 years.

Regards, Nintendokater

Offline gerrit

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« Reply #4 on: August 14, 2019, 03:37:24 AM »
Pretty much any system of dynamical equations that is nonlinear and has more than 3 variables exhibits chaotic behaviour, which means it "is" fractal in the sense of attractors ("strange" attractors).

Known fundamental physics laws (say standard model + gravity) fits that, so as far as we know the universe "is" a fractal. I think that is kinda obvious and does not give any particular insight.

I do think fractals as we consider them here (Mandelbrot set + generalizations) do give some insights in the real world but not in such an obvious way. I have a coffee house philosophy on it which I may ramble out here later when I feel like it, now going to watch a severe thunderstorm and wonder about fractal dimension of lightning.

Offline Tas_mania

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« Reply #5 on: August 28, 2019, 02:29:36 AM »
Good replies here both for and against the original question. I like the 'coffee house' position that is probably closer to the truth. A thunderstorm is a complex system that may or may not have anything to do with fractals but it's awesome anyway.

The galactic universe may as well be a fractal because humans don't really understand it. Closer to our home planet nature often behaves like a fractal but it cannot be proven that it is.

Did the universe create fractals or did fractals create the universe? I found the 'Mathematical universe hypothesis'
https://en.wikipedia.org/wiki/Mathematical_universe_hypothesis

I like Tegmarks description - 'observers, including humans, are 'self-aware substructures'.


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