These kind of fractal have actually 4 dimentional structure since c_x and c_y can also be parameters. I'd love to see their slice as 3D, but have yet to find a good way to visualize them...
“Burning Ship” fractal
31–40 of 75 posts
Re: “Burning Ship” fractal
#32Incredibly creepy. What if one day we found a fractal that contains a message from God?
It would be like finding the face of Jesus on a piece of toast, or the face of an alien on a satellite image of Martian surface. (Both of which were actual images that gathered some cult following in their time.) Spend enough time applying human interpretation to non-human processes, and something will eventually come up that tickles your senses.
When I was a kid I had a sound editing application (think of something like audacity) and it had a tool to generate white noise. I was deathly afraid of generating white noise and then slowing it down because I thought that I may find hidden messages.
Re: “Burning Ship” fractal
#33I miss FRACTINT.
I just thought the same, but guess what: Their Website still exists (https://www.fractint.org/) and the last binary package is from April this year :)
Re: “Burning Ship” fractal
#34These kind of fractal have actually 4 dimentional structure since c_x and c_y can also be parameters. I'd love to see their slice as 3D, but have yet to find a good way to visualize them... https://i.imgur.com/JRfLy6R.mp4
> These kind of fractal have actually 4 dimentional structure since c_x and c_y can also be parameters
They're not parameters in that sense.
The fractal is computed by taking each point on the plane as coordinates (c_x, c_y), and then iteratively applying the recursion relation. Then, with luminosity depending on how quickly that sequence escapes to infinity, we color in that point (c_x, c_y) in our image.
Re: “Burning Ship” fractal
#35Incredibly creepy. What if one day we found a fractal that contains a message from God?
I play around with fractals a lot and once I fiddled with mandelbrot and found something that resembled a pig running on two legs.
I guess it would be called the running pig fractal.
This might be a message from god: don't eat pork.
Re: “Burning Ship” fractal
#36Earlier quoted context omitted.
This is crazy. How do they pilot the zooming of the fractal? It must be carefully planned and programmed in to generate the video. edit: I guess if they find an interesting thing very zoomed-in, then zoom out from that, the whole video will be interesting.
I'm not sure your edit is right. No reason why there can't be a tiny but very complex thing which looks single-colour at the next 1 or 10 or 100 orders of magnitude. But there are an infinite number of very interesting things in this fractal. If you constantly zoom in on interesting looking areas, you will find this kind of complexity with minimal need for backtracking.
I'm guessing most fractals don't have a smooth boundary anywhere, so if you know any boundary point, you can zoom in on it and it'll be "interesting."
Re: “Burning Ship” fractal
#37Xaos [1] is great for exploring fractals and the Burning Ship is no exception -- just define a user formula of
powi(rabs(z)+i*rabs(im(z)),2)+c
;Position file automatically generated by XaoS 4.2.1
; - a realtime interactive fractal zoomer
;Use xaos -loadpos to display it
(initstate)
(filter 'anti #t)
(palette 2 73629707 0)
(formula 'user)
(usrform "powi(rabs(z)+i*rabs(im(z)),2)+c")
(usrformInit "0")
(maxiter 5000)
(bailout 5)
(view -1.6924 -0.02769 0.1137 0.1137)
[1] https://github.com/xaos-project/XaoS [2] https://i.imgur.com/mJ0uZG7.png
Re: “Burning Ship” fractal
#38Earlier quoted context omitted.
If you replace the complex numbers with split-complex numbers, then the set of holomorphic functions becomes uninteresting. You therefore need to use * (meaning the split-complex analogue of complex conjugation) to get anything interesting. It follows that the obvious analogue of complex analysis over the split-complex numbers is pretty sterile, but I think that the split-complex numbers themselves remain interesting…
Complex conjugation is non-holomorphic and yes, it's ugly. I still don't see why it being useful as a construction makes it a beautiful operation in analysis given that it isn't algebra. There are holomorphic split-complex functions and they aren't uninteresting at all - they are quite beautiful and complex, relating to wave equations: https://en.wikipedia.org/wiki/Motor_variable#D-holomorphic_f... They're not someth…
Here's the split-complex Mandelbrot (and Mandelbar for comparison): https://imgur.com/a/j2c7qkB
Read my other reply.
Re: “Burning Ship” fractal
#39I've experimented with the "Mandelbar" (sometimes called the "tricorn") fractal over the split-complex numbers: https://imgur.com/PkzY7B6 The result isn't completely trivial, but isn't particularly impressive either. Anybody want to try Burning Ship over the split-complex numbers? It looks like you only need to replace the complex "i" with the split-complex "j".
Here it is. Split-complex burning ship using Xaos: https://imgur.com/a/tBTuUDV This is my first time using that program. It doesn't look too bad. Same thing, but with the dual numbers: https://imgur.com/a/kTU5ztn
A follow-up question, not easily answered using Xaos: The dual numbers can be pictured as lines in the Euclidean plane instead of points (details here: https://en.wikipedia.org/wiki/Laguerre_transformations). What would the above "dual number burning ship" look like?
Re: “Burning Ship” fractal
#40Earlier quoted context omitted.
I'm not sure your edit is right. No reason why there can't be a tiny but very complex thing which looks single-colour at the next 1 or 10 or 100 orders of magnitude. But there are an infinite number of very interesting things in this fractal. If you constantly zoom in on interesting looking areas, you will find this kind of complexity with minimal need for backtracking.
I'm guessing most fractals don't have a smooth boundary anywhere, so if you know any boundary point, you can zoom in on it and it'll be "interesting."
Yeah I think you're right mike_hock.
On top of that I think that locations on (or near) the boundary, tend to stay on the boundary (and stay in the center of the image too) when zooming out.
While purely zooming (not translating) to a known boundary (or near) point, you won't ever see a move to another section-of-boundary, so if there are both 'inside' and 'outside' regions, corresponding to attractors at 0 and infinity, (the 2 main ones in these types of fractals) in the most-zoomed in state, then there will always be regions of both states contained in the final image when zoomed out (until you get to the 'top').
Maybe it would be possible for there to be formulae that don't hold to this? If the fractal had an incredibly sparse structure, say? To be honest I'm more interested in the opposite myself: Structures where the boundary (between N regions or behaviors) is so wiggly, it's almost 2 dimensional itself!. (If anyone wants to read more, I've called one particular interesting example of this: 'mandelfield' on UltraIterator)