Burning Ship Fractal • Hacker News Board

Re: Burning Ship Fractal

#61

Post by spacehome » Tue, Sep 27, 2016, 8:32 AM UTC

sp332 wrote: post #16

jawarner wrote: post #2

I'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).

For the Mandelbrot set, I'm familiar with the proof that says that if |z_n| > 2, then 0 iterates to infinity regardless of c. The proof depends on it being an analytic function. How do you know that's also true for this equation?

Re: Burning Ship Fractal

#62

Post by spacehome » Tue, Sep 27, 2016, 8:34 AM UTC

Chinjut wrote: post #31

qubex wrote: post #28

Earlier quoted context omitted.

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?

Of course it's relevant. qubex is just confused.

Re: Burning Ship Fractal

#63

Post by frou_dh » Tue, Sep 27, 2016, 9:07 AM UTC

SOLAR_FIELDS wrote: post #40

frou_dh wrote: post #26

Earlier quoted context omitted.

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.

The risk with procedurally generated stuff is that it can feel adequate but soulless to the game player.

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.

Re: Burning Ship Fractal

#64

Post by qubex » Tue, Sep 27, 2016, 9:20 AM UTC

jerf wrote: post #45

qubex wrote: post #28

Earlier quoted context omitted.

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 mean by not having a constructive algorithm to produce primes. The Sieve of Eratosthenes will output any given prime, with the primes coming out in order, given enough time. There may not be an efficient algorithm, but for most definitions of "information" that won't matter. The sequence of all primes is both so richly structured we've probably only scratched the surface and almost entirely bere…

Yup you're right and I'm wrong.

Re: Burning Ship Fractal

#65

Post by djaychela » Tue, Sep 27, 2016, 9:56 AM UTC

nitrogen wrote: post #59

frou_dh wrote: post #26

Earlier quoted context omitted.

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.

Was Fractal Lab ever made available to the public?

Author says no at the bottom of the video... there's something similar (and more basic) here:

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!)

Re: Burning Ship Fractal

#66

Post by kozak » Tue, Sep 27, 2016, 9:57 AM UTC

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?

Now that we are 5 years in future, it would be cool if someone re-rendered it in higher resolution, 60 fps and with better antialiasing.

Re: Burning Ship Fractal

#67

Post by sp332 » Tue, Sep 27, 2016, 12:02 PM UTC

spacehome wrote: post #61

sp332 wrote: post #16

Earlier quoted context omitted.

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).

For the Mandelbrot set, I'm familiar with the proof that says that if |z_n| > 2, then 0 iterates to infinity regardless of c. The proof depends on it being an analytic function. How do you know that's also true for this equation?

Interesting point! I don't know if it's really true, but that's how the fractal images seem to be generated.

Re: Burning Ship Fractal

#68

Post by pault » Sat, Oct 01, 2016, 10:25 PM UTC

nitrogen wrote: post #59

frou_dh wrote: post #26

Earlier quoted context omitted.

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.

Was Fractal Lab ever made available to the public?

I don't understand how someone could spend so much time on an obviously excellent product and not want to show it off to the world.