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Burning Ship Fractal

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Re: Burning Ship Fractal

#31

Post by Chinjut »

qubex wrote: post #28
schoen wrote: post #21

Earlier quoted context omitted.

> Why are simple expressions not simple in all "natural" representations? Another example might be the primes, which have a very simple description and very subtle structure in their distribution.

I don't really agree that the primes “have a very simple definition” in that the notion of ‘primeness’ is one of satisfiability and no constructive algorithm is known to exist.

I'm not sure what you're getting at here. Is it not relevant that there is a simple algorithm to enumerate the primes, or, even more so, determine whether a given value is prime?

Re: Burning Ship Fractal

#32

Post by jacobolus »

pfortuny wrote: post #8
wyager wrote: post #4

Earlier quoted context omitted.

I agree. It's very strange that extremely simple, very fundamental functions lead to such stochastic-looking nonsymnetric behavior. Where does all that "entropy" come from? It's certainly not hidden in any big numbers in the fractal definition.

It comes from the aperiodic structure of real numbers (that is a weird and wrong expression but I cannot find a better way to explain it). Nonrational real numbers are inherently chaotic as seen from the inside (even rational numbers might be seen as such). Real numbers are weird. Totally. Also the fact that you are defining something depending on convergence makes it even weirder, as limits do not tend to commute wi…

There are no non-rational “real” numbers involved whatsoever in drawing this fractal (or e.g. the Mandelbrot set). Only rational numbers, simple purely rational functions, and some amount of truncation of the least significant bits at each step.

The deep “weird” “inherently chaotic” structure you’re talking about is the structure of the rational numbers.

Re: Burning Ship Fractal

#33

Post by tapatio »

frou_dh wrote: post #26
carlbarrdahl wrote: post #5

7 minute zoom of the fractal. Incredible level of detail and that final mirrored inverted fractal at 6'38 took me by surprise. https://www.youtube.com/watch?v=CD9yNFmb2FE Are there any good fractal explorers in VR?

Not quite VR, but there exists someone's personal hobby 3D fractal viewer that has an absolutely bananas level of polish: http://sub.blue/fractal-lab I highly recommend taking the time to watch his video.

That is amazing. Thanks for sharing.

Re: Burning Ship Fractal

#36

Post by foobarian »

carlbarrdahl wrote: post #5

7 minute zoom of the fractal. Incredible level of detail and that final mirrored inverted fractal at 6'38 took me by surprise. https://www.youtube.com/watch?v=CD9yNFmb2FE Are there any good fractal explorers in VR?

That is insane. How is it possible to zoom in that far? Looks like it would have to use some kind of big number library and then parallelize the heck out of it.

I like how the rest of the page seemed to zoom out when I glanced outside the video after watching a few minutes or so.

Re: Burning Ship Fractal

#37

Post by [deleted] »

foobarian wrote: post #36
carlbarrdahl wrote: post #5

7 minute zoom of the fractal. Incredible level of detail and that final mirrored inverted fractal at 6'38 took me by surprise. https://www.youtube.com/watch?v=CD9yNFmb2FE Are there any good fractal explorers in VR?

That is insane. How is it possible to zoom in that far? Looks like it would have to use some kind of big number library and then parallelize the heck out of it. I like how the rest of the page seemed to zoom out when I glanced outside the video after watching a few minutes or so.

[deleted]

Re: Burning Ship Fractal

#38

Post by warbiscuit »

foobarian wrote: post #36
carlbarrdahl wrote: post #5

7 minute zoom of the fractal. Incredible level of detail and that final mirrored inverted fractal at 6'38 took me by surprise. https://www.youtube.com/watch?v=CD9yNFmb2FE Are there any good fractal explorers in VR?

That is insane. How is it possible to zoom in that far? Looks like it would have to use some kind of big number library and then parallelize the heck out of it. I like how the rest of the page seemed to zoom out when I glanced outside the video after watching a few minutes or so.

I think this is a youtube upload of one of the animations from http://www.hpdz.net/ -- there's a ton others on there too.

They go into the techniques a bit on the site under the "technical" section.

Re: Burning Ship Fractal

#39

Post by lmm »

wyager wrote: post #18
jerf wrote: post #15

Earlier quoted context omitted.

"Where does all that 'entropy' come from?" Your scare quote suggests you may already know this, but for the benefit of others, the answer is that there isn't any. Fractals may look visually complicated, but their information content is fully captured by the routines used to generate them, which include the formula and the coloring system being used. This is one of the ways in which "information" is a highly counter-i…

Yes, that is what I mean. Why is there a disconnect between the complexity of the compact description and the naive description? Why are simple expressions not simple in all "natural" representations? This is not addressable with the contrived example of "you can create an encoding scheme that reduces an arbitrarily complex description to an arbitrarily short identifier". After all, this is not a constructed compress…

> This is not addressable with the contrived example of "you can create an encoding scheme that reduces an arbitrarily complex description to an arbitrarily short identifier". After all, this is not a constructed compression scheme. Why does nature expand simple expressions to these particular complicated forms?

If not these particular forms then it would be some others. That fractals exist is pretty-much the fact that pseudo-random number generators exist: you plug in a small amount of input and it generates noise. The fact that it looks like something is more a sign of the overactive human facility for pattern recognition than anything else. (Also I suspect it would look a lot less like a burning ship if we hadn't been told it was a burning ship)

Re: Burning Ship Fractal

#40

Post by SOLAR_FIELDS »

frou_dh wrote: post #26
carlbarrdahl wrote: post #5

7 minute zoom of the fractal. Incredible level of detail and that final mirrored inverted fractal at 6'38 took me by surprise. https://www.youtube.com/watch?v=CD9yNFmb2FE Are there any good fractal explorers in VR?

Not quite VR, but there exists someone's personal hobby 3D fractal viewer that has an absolutely bananas level of polish: http://sub.blue/fractal-lab I highly recommend taking the time to watch his video.

I believe that doing this for procedural generated games along the lines of No Man's Sky is the true future of where we can go for randomly generated worlds. Since a lot of planetary formation patterns we observe here on earth follow fractal-esque patterns, this would be a great application for a powerful generator like this one.
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