I've had a few major complications in my life, so sorry for the looong delay.
The mapping is conformal so shapes of (small) things stay the same but they exist at every scale.
Consequently there are a limited number of fractal forms that can exist...
a curve becomes a logarithmic spiral
a junction (like a Y shape) becomes a logarithmic tree
a loop becomes a 'sponge' / apollonian gasket type thing (bubbles / nets)
a single blob becomes a 'cluster' of blobs
etc
...
I made an attempt to classify these forms for 2d and 3d here:
https://sites.google.com/site/simplextable/ by ignoring the exact shape and looking more at its connectivity, a bit like topology does.
Thank you very much Tglad!
This cleared up a lot.
From that point of view, one might call the mandelbrot set a multifractal, as most of the basic fractal patterns can be found in it..
nice!
I also love your shape classifications and think that this is outstanding work you did there!
There is nobody on this planet that can answer your question.
I'm pretty sure there is, but if he told me, I probably wouldn't believe him.. at least if he doesn't try it in a scientific way...
Thank you Mandelbrot you made my life so much better.
Word.
what a trailblazer he was...
We clearly live in a completely fractal universe - that's clearly a computer simulation. There is plenty of compelling proof of this:
....
We live in a holographic clearly computer simiuation, hence nature is obviously fractal in nature. It's computer code.
I have a serious problem using our human terms "computer & simulation" in this context.
they seem to degrade the awesome beauty of the cosmos (though I'm sure that's not what you're trying to do.
)
I too firmly believe that the universe is the result of an ongoing recursive process.
But I think that math and calculation is just a very usefull language to express what is happening. but not more. Content is king, not the language that we use to describe it...
And consciousness! How can the one thing that is fundamentally central for YOU be completely "ignored" by science?
Math, a simulation without consciousness, without an observer is nothing. it's only virtual.
(I recommend a youtube search for Peter Russel - primacy of consciousness, a real eye opener in that area)
Btw, have you heard of Konrad Zuse and his idea of calculating space?
http://en.wikipedia.org/wiki/Calculating_SpaceYou just have to learn to cut code and draw these fractals and get first hand experience, how the iterations over time create complexity.
doing that certainly helps. but it's not the only way. I've come from the other direction, the strictly visual. as you described how it happend for you, I just started to recognize these patterns one day. and since then discovered them in many more places, were I think they are still hidden for most.
the really hard part is to find a language besides deep math, that helps interested people to see and discover it on their own, without having to work hard and think about it for years..