Fractal universe

[SleepingTroll]

I believe the universe is infinite, in such a universe eventually there would be repetition of repetition ad infinitum, it would resolve to a fractal!
I also believe the the most primitive constituent entity of the universe is an expanding toroidal field.
I am not a mathematician, however, I would like to find one that feels they could combine the two, any takers?

[Chillheimer]

I'm definitely with you.
Fractals span into every aspect of our life and the universe.
I'm on a path to collect all this and fit it together as there seems to be no good source that has already done this. at least not as comprehensive as i think the fractal universe is.

here's my "notepad" so far:
http://www.pinterest.com/chillheimer/life-is-fractal/

sadly, I'm not a mathematican too.
 but then again, I don't think this is really necessary to see all that.

I believe the universe is infinite, in such a universe eventually there would be repetition of repetition ad infinitum, it would resolve to a fractal!

VS.

I also believe the the most primitive constituent entity of the universe is an expanding toroidal field.

I think these two statements contradict.
if repetition follows upon repetition, if it's really fractal, there can't be such thing as the "smallest entity"

[Kalles Fraktaler]

I think these two statements contradict.
if repetition follows upon repetition, if it's really fractal, there can't be such thing as the "smallest entity"

Why? Fractal is applied on things I think. If it is applied on numbers, which can be infinite, it can be infinite. If it is applied on physics or biology, there can be a smallest entity and not infinite. But still fractal. Or?

[Chillheimer]

Why? Fractal is applied on things I think. If it is applied on numbers, which can be infinite, it can be infinite. If it is applied on physics or biology, there can be a smallest entity and not infinite. But still fractal. Or?

mhh.. yes. you got me there.. somehow..
but the way the sleeping troll wrote it, he talked of the universe being infinite...
as long as we keep discovering smaller parts (and think they are the smallest for some years, until the next smaller part is found) I'm not really sure..

I think that, if the universe is as fractal as I personally believe, it keeps going infinite, or a cycle will close/restart at some point, like a minibrot.
but that is just my personal believe based on some observation, thinking and instinct.. so not at all scientific..

[kram1032]

Fractals are not applied on numbers.
Fractals are defined sets of, usually, numbers.
Usually, they are defined through recursion of some sort but sometimes you might arrive at them by other means.

That being said, the term "fractal" never really was made precise.

[Kalles Fraktaler]

To me the fascinating thing with fractals is that complex patterns arise on the border between invariant order and noisy chaos.
Inside the Mandelbrot set there is order, outside there is chaos, and between, on the border, complex patterns arise.
Out in cold space there is order, inside the sun there is chaos, and between, where the earth is, complex patterns arise.
Whenever a system, any system, contains order and chaos, fractals - complex patterns, arise on the border between the extremes.
The predictable fractals that must include recursion and are built with specific rules to create a specific result is not that fascinating I think.
Because I believe that the border between order and chaos explains something about the reason why we are here.

[kram1032]

How are "fractals that must contain recursion" predictable? The Mandelbrot Set is defined via recursion.

[Chillheimer]

Fractals are not applied on numbers.
Fractals are defined sets of, usually, numbers.

kalle said "IF they are applied on numbers"
I think that numbers, math is just one of many languages to 'communicate' the universal concept of fractals.

That being said, the term "fractal" never really was made precise.

Yes, and that really seems to be a problem as I've encountered in many discussions here. Everyone defines "fractal" in a slightly different way. hehe, in a self similar way - appropriately that's quite fractal, isn't it?
I wish there was that ONE definition of what fractal is. But then again it would have to be comprehensive enough to include further discoveries and not just math..
http://www.fractalforums.com/fractals-in-nature/search-for-an-agreeable-definition-of-fractals-in-nature/msg68292/#msg68292

Out in cold space there is order, inside the sun there is chaos, and between, where the earth is, complex patterns arise.
Whenever a system, any system, contains order and chaos, fractals - complex patterns, arise on the border between the extremes.

Nice! Never thought of it this way..

Because I believe that the border between order and chaos explains something about the reason why we are here.

Yes..
Although I'm quite sure we won't ever find the abolute WHY, but definitely find out more about the HOW and based on that, what to do or what to strive for in life.
And I love that this makes it possible to gain spiritual insights with the use of science instead of dogmatic religion.

I believe Fractals have the potential to bring together science, philosophy and spiritualism without having to declare any of them as wrong.
And I'm pretty sure that this will manifest in the next years..

Here's a guy who thought that through and comes to the same conclusions as I do´(but can communicate it in a better way than I could)
<a href="http://www.youtube.com/v/axaH4HFzA24&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/axaH4HFzA24&rel=1&fs=1&hd=1</a>
but be warned. the amount of information is very exhausting and overwhelming. I had to watch it in several sessions.
(the spiritual part starts at about 1:37:00 but I recommend to watch the whole thing to get enough background)

[Kalles Fraktaler]

How are "fractals that must contain recursion" predictable? The Mandelbrot Set is defined via recursion.

I was thinking about mountains, snowflakes, trees and other simple predictable patterns of classical recursive fractals that doesn't contain the chaos part.

[kram1032]

Mountains are shaped by weather and plate tectonics. There isn't much that is more chaotic than weather.
Snowflakes form in a chaotic manner too.
Trees follow several rules to remain adaptive under a wide variety of conditions from droughts over harsh winters to strong winds (storms). They do so recursively, for instance thickening those branches that are most stressed by a current storm. And the rules underlying their branching patterns also are recursive. All in all, this also can give quite some chaotic behavior.

[Kalles Fraktaler]

Mountains are shaped by weather and plate tectonics. There isn't much that is more chaotic than weather.
Snowflakes form in a chaotic manner too.
Trees follow several rules to remain adaptive under a wide variety of conditions from droughts over harsh winters to strong winds (storms). They do so recursively, for instance thickening those branches that are most stressed by a current storm. And the rules underlying their branching patterns also are recursive. All in all, this also can give quite some chaotic behavior.

Sorry if I was not clear enough, here is an example so that you can understand what I mean:
http://en.wikipedia.org/wiki/Koch_snowflake
A real snowflake is of course more interesting, probably since it contains some chaos, which Koch's snowflake don't.

[kram1032]

Ah, now I understand.
Just to be clear, even in real life, the universe is fundamentally recursive in nature. What ever current state you have, as measured across the entire universe, goes through a very specific set of rules which transform the current moment into the next. So in a sense we are all defined through some sort of recursion.
That being said, I agree that fractals like the Mandelbrot set, that split regions of bounded order and exponential growth to infinity with a border of complexity, are more interesting than simpler ones like the Sierpinski triangle or some Cantor foam, and that real life typically is of this more complex type.

Most real-life examples of fractals are actually multifractals.

[Kalles Fraktaler]

Ah, now I understand.
Just to be clear, even in real life, the universe is fundamentally recursive in nature. What ever current state you have, as measured across the entire universe, goes through a very specific set of rules which transform the current moment into the next. So in a sense we are all defined through some sort of recursion.
That being said, I agree that fractals like the Mandelbrot set, that split regions of bounded order and exponential growth to infinity with a border of complexity, are more interesting than simpler ones like the Sierpinski triangle or some Cantor foam, and that real life typically is of this more complex type.

Most real-life examples of fractals are actually multifractals.

Deep space order and hot sun chaos, and on the thin border in between the recursion of life and death and natural selection created complex fractals called humans. Mind blowing and beautiful

[Chillheimer]

Most real-life examples of fractals are actually multifractals.

That stuck me too some time ago. And that (in my opinion) shows scientifically how EVERYTHING is fractal. literally.
And I believe that the implications are as huge as the implications of 'single fractals' are.

And I find it hard to understand how it can be that science doesn't care about this.

I mean, there isn't even a german wikipedia article for multifractal systems.
And the english one is full of a micro-view, no one looks at the overall-everything-multifractal system, realizing that it is ONE huge thing!

Yeah, this sounds esoteric. everything is one.

But this is an exoteric approach! it can be proven scientifically
(I'm sure, but this is not an easy task)

[kram1032]

These things are not ignored. It's just that fractals are very hard to describe. Our most powerful mathematical systems are, as of yet, barely capable of dealing with fractals in detail.
But progress is constantly being made. We are coming up with new tools to deal with complexity all the time.

Here, for instance, is some new research on swarm intelligence which uses new methods of measurement to extract more information to build better models of, in this case, schools of fish, swarms of insects or flocks of birds. http://www.newscientist.com/article/mg22129540.800-mind-meld-the-genius-of-swarm-thinking.html