Burning Ship Fractal
en.wikipedia.org
en.wikipedia.org
https://www.youtube.com/watch?v=CD9yNFmb2FE
Are there any good fractal explorers in VR?
I wonder how they chose the point; trial and error, or was there some mathematical way of guaranteeing that there is something "interesting" at that point?
That page is older, but based on the performance at the time I'm still not sure you could render them in sufficient real-time to make VR a useful thing.
(I leap to the assumption you're referring to 3D fractals because merely adding VR to a 2D fractal viewer does not seem like a useful thing to do.)
http://www.hpdz.net/TechInfo/CameraTilt.htm
you can imagine the compelxity of introducing perspective into the already computationally heavy fractal calculations
I highly recommend taking the time to watch his video.
There can be a hybrid approach where, at development time, a bunch of procedurally generated assets are cranked out, and then a human artist hand-picks the best specimen and uses it as a starting point for a manually created asset.
http://hirnsohle.de/test/fractalLab/
I always find it a pity when I see something as inspiring as this that's not available to use (even without any support), but I guess that's the author's prerogative... (sadly!)
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.
They go into the techniques a bit on the site under the "technical" section.
Utterly devastate the computational ability of your CPU. I remember setting up my and k6 300mhz to compute stuff sometimes for days to get awesome fractal deep zooms like this. The computation is embarrassingly parallel but no hardware handles numbers that precise with any reasonable speed. Something like 1024 bit floating point in fractint back in the day. I'd love to see an efficient GPU implementation of that kind of stuff
even just bounds at the edges of the visualised space would help to illustrate the phenomenon.. also, the utilised color key would further illuminate
"The deepest and first ever HD deep-zoom animation into the Burning Ship fractal. This is one of the creepiest and yet stunningly gorgeous fractals ever."
I agree about the creepy factor. I've seen many a fractal video, but this one... is different. Maybe it's the music, but it really did feel mysterious and... creepy.
Thanks for posting the link.
I wouldn't be surprised if the burning ship fractal could be coded on dwitter (i.e. with 140 characters or less) as well
t?i++:i=0;for(j=1080;j--;){a=b=0;k=35;for(;k--&&a*a+b*b<4;)c=a*a-b*b+i/540-2,b=2*(a*b<0?-a*b:a*b)+j/540-1,a=c;x.fillRect(i,j,1,S(k/9))}As an afternoon exercise, I wrote a Mandelbrot draw function (my first fractal display code!). Then I realized it was both faster and used less code and runtime memory than the image display stuff, so I replaced it in my environment. Other people were amused by it, so it went in public repository.
A couple weeks later, someone removed it to reinstate the image display. I guess having the company logo for internal-only code was more important to someone :(
I don't work there anymore.
https://en.wikipedia.org/wiki/File:American_Megatrends_Logo....
If I remember correctly, early AMIBIOS did generate that logo procedurally using a short piece of code.
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 with anything unless smooth conditions take place. And for these fractals, there is no smoothness near the "border".
In my view, the real source of complexity is the fact that the algorithm can use arbitrary iterations to magnify small differences. It's the unpredictable nature of computing machines, not real numbers. The nature of real numbers is only a guide to developing and explaining that underlying complexity.
Perhaps the interesting thing is that the set of n-bit programs expands to only 2^n possible outputs. Why are some finite number of infinite-length outputs accessible, but not others? Why does nature favor those sequences?
Are they though? A 5-state Turing machine might seem trivial, but there exist programs in it, that we don't know if they ever halt or not [1]. Their behavior is totally non-deterministic for our understanding. There are also minimalistic cellular automata that produce completely unpredictable patterns. [2]
[1] https://en.wikipedia.org/wiki/Busy_beaver#Known_values_for_....
The deep “weird” “inherently chaotic” structure you’re talking about is the structure of the rational numbers.
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-intuitive quantity for people. Very small numbers of bits in a given encoding scheme can produce incredibly complicated pictures, but there's still no more information that what was put in to start with. Simply looking at something and going "Yup, that's complicated" does not mean it has a lot of information in it.
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?
Another example might be the primes, which have a very simple description and very subtle structure in their distribution.
I think because that simple description describes a non-linear iterative process that feeds back on itself.
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)
My point is basically, the system includes the interpreter all the way up to the eye and the mind, and it seems tricky to completely detach such context from a description of how 'complex' things are.
People arguing about the complexity of the human brain (especially those that know a lot about the way it works) fall into this trap constantly, and it drives me nuts: there's a ton of structure, but proportionally negligible information in the brain's programming.
http://www.pouet.net/prod.php?which=54663
Unfortunately, that demo is not that portable, and I was unable to find a video of it.