Burning Ship Fractal

#1

Post by dedalus » Mon, Sep 26, 2016, 1:25 PM UTC

Burning Ship Fractal
en.wikipedia.org

Re: Burning Ship Fractal

#2

Post by jawarner » Mon, Sep 26, 2016, 4:48 PM UTC

I'm always fascinated by how simple functions like this generate complex behavior when iterated.

Re: Burning Ship Fractal

#3

Post by hahamrfunnyguy » Mon, Sep 26, 2016, 4:53 PM UTC

....There's a fractal for that!

Re: Burning Ship Fractal

#4

Post by wyager » Mon, Sep 26, 2016, 4:55 PM UTC

jawarner wrote: post #2

I'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.

Re: Burning Ship Fractal

#5

Post by carlbarrdahl » Mon, Sep 26, 2016, 5:04 PM UTC

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?

Re: Burning Ship Fractal

#6

Post by moridin » Mon, Sep 26, 2016, 5:07 PM UTC

Anyone else thing that the Julia set diagram of this looks like a Nazca-line Image? Imagine you reverse engineered the Nazca Images on the ground and they described advanced Mathematics...Sci-Fi short story Idea there for sure :D

Re: Burning Ship Fractal

#7

Post by pavel_lishin » Mon, Sep 26, 2016, 5:11 PM 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?

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?

Re: Burning Ship Fractal

#8

Post by pfortuny » Mon, Sep 26, 2016, 5:16 PM UTC

wyager wrote: post #4

jawarner wrote: post #2

I'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.

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 with anything unless smooth conditions take place. And for these fractals, there is no smoothness near the "border".

Re: Burning Ship Fractal

#9

Post by rhubarbquid » Mon, Sep 26, 2016, 5:17 PM UTC

I started working on a web based renderer for the burning ship fractal a little while ago. It's far from perfect, I still consider it a WIP, but it works well enough to play around with: http://stevenmcdonald.github.io/fractals/burning_ship/

Re: Burning Ship Fractal

#10

Post by iverjo » Mon, Sep 26, 2016, 5:21 PM UTC

Fractals 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