Hah. I would guess that this made its way here because someone posted one on ShaderToy recently.
See: https://www.shadertoy.com/view/XtKGDD
Burning Ship Fractal
11–20 of 68 posts
Re: Burning Ship Fractal
#127 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?
Fractals and 3D are an interesting problem: http://www.skytopia.com/project/fractal/mandelbulb.html
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.)
Re: Burning Ship Fractal
#137 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?
I'm sure they picked the point they're zooming in on intentionally, but I thought it was interesting when it started being radially symmetrical. 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?
As long as you keep to the "edge" of the set, I think you're guaranteed to find interesting things wherever you go. I presume this zoom was guided, the exact zoom position manually adjusted every once in a while based on what comes up.
Re: Burning Ship Fractal
#14Fractals can be drawn by surprisingly small amounts of code. For example, this mandelbrot fractal is implemented in 122 characters of JavaScript: https://www.dwitter.net/d/123 I wouldn't be surprised if the burning ship fractal could be coded on dwitter (i.e. with 140 characters or less) as well
Just need to add a Math.abs: https://www.dwitter.net/d/457
Re: Burning Ship Fractal
#15I'm always fascinated by how simple functions like this generate complex behavior when iterated.
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.
"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-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.
Re: Burning Ship Fractal
#16I'm always fascinated by how simple functions like this generate complex behavior when iterated.
The color of each point is the number of iterations it takes to "escape" past the (-2-2i, 2+2i) barrier. So if you start at a point and iterate 3 times before escaping, it gets one color. If you start at a different point and have to iterate 4 times, then it gets the next color. All the colored pixels are outside the Mandlebrot set, and all the black pixels are inside (or you haven't done enough iterations to know).
Re: Burning Ship Fractal
#17Earlier 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…
While "real" numbers are indeed weird, I don't think that's the real explanation here. There are lots of small programs with complex output that have nothing to do with real numbers. If someone gave you one of these programs without telling you what it was for, real numbers would at best be a useful abstraction (bear in mind that there are no actual "real numbers" here, only finite bit-strings). But it might turn out to be the equivalent of a stream cipher, instead. That would, if done correctly, have even more apparent entropy than your typical fractal, which at least has some higher-level structure.
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.
Re: Burning Ship Fractal
#18Earlier 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.
"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 compression scheme. Why does nature expand simple expressions to these particular complicated forms?
Re: Burning Ship Fractal
#19Earlier quoted context omitted.
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…
While "real" numbers are indeed weird, I don't think that's the real explanation here. There are lots of small programs with complex output that have nothing to do with real numbers. If someone gave you one of these programs without telling you what it was for, real numbers would at best be a useful abstraction (bear in mind that there are no actual "real numbers" here, only finite bit-strings). But it might turn out…
But computing machines aren't unpredictable. They are very predictable. They appear to pull complex structure out of the aether.
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?
Re: Burning Ship Fractal
#207 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?
I'm sure they picked the point they're zooming in on intentionally, but I thought it was interesting when it started being radially symmetrical. 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?
Or they recorded it zooming out, and reversed the recording.