extending Mandelbox fractals with shape inversions

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Offline CozyG

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« on: September 08, 2018, 05:20:09 AM »
I'm excited to share with fractalforums that I recently published a peer-reviewed paper, "Extending Mandelbox Fractals with Shape Inversions", in the proceedings of the Bridges 2018 math/art conference!  The conference was in Stockholm near the end of July, but I've been holding off on posting about this until now so I could also get a slightly modified version up on arXiv.org, and get my github repo presentable.

Abstract:
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The Mandelbox is a recently discovered class of escape-time fractals which use a conditional combination of reflection, spherical inversion, scaling, and translation to transform points under iteration. In this paper we introduce a new extension to Mandelbox fractals which replaces spherical inversion with a more generalized shape inversion. We then explore how this technique can be used to generate new fractals in 2D, 3D, and 4D.

This is really a continuation of the work I posted about last year in the old fractalforums group: Generalized shape inversion applied to the Mandelbox. But with a lot more development since then.

Here are additional links to the arXiv version of the paper, and to the github repo. Fragmentarium fragments for shape inversion Mandelbox images in the paper are in the repo under fragmentarium/bridges_2018_mandelbox_paper. If you want to try some out and prefer a downloadable zip, I've attached a current snapshot. But I'm planning to add a lot more example frags to the repo.

And here's a few example images from the paper. These are both 3D slices through different 4D Mandelboxes, with shape inversions that are mixtures of hyperspheres and hypercubes:




« Last Edit: September 08, 2018, 05:30:44 AM by CozyG, Reason: adding zipped files as attachment again »

Offline 3DickUlus

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« Reply #1 on: September 08, 2018, 08:44:29 AM »
 :bananalama: very cool!

Inspires me to keep working on Fragmentarium ;)
Resistance is fertile... you will be illuminated!

https://en.wikibooks.org/wiki/Fractals/fragmentarium

Offline fractower

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« Reply #2 on: September 09, 2018, 05:17:47 PM »
I had done something similar a few years ago. It is available in mandelbulber as "generalized box fold".

http://www.fractalforums.com/amazing-box-amazing-surf-and-variations/generalized-box-fold/

Offline mclarekin

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« Reply #3 on: September 10, 2018, 11:44:32 AM »
@cozyG, images look great O0



@fract tower . Thanks for the Generalized Box Fold in Mandelbulber. 2010 was long time ago,   I only found fractal forums in 2013, so I missed out on the cool development that was happening in those earlier days.

Offline CozyG

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« Reply #4 on: September 10, 2018, 01:36:57 PM »
I had done something similar a few years ago. It is available in mandelbulber as "generalized box fold".

http://www.fractalforums.com/amazing-box-amazing-surf-and-variations/generalized-box-fold/

I think the two approaches have similarities, but they modify different parts of the Mandelbox algorithm. As I understand it, the generalized box fold modifies reflections in the "BoxFold" step of the algorithm, whereas shape inversion modifies spherical inversion (and/or minimum radius) in the "SphereFold" step.

Both approaches share a common geometric concept of replacing one shape for another. This allowed me to translate and reuse part of your excellent generalized box fold code when I needed intersection calculations for the non-cube Platonic solids (tetrahedron, octahedron, icosahedron and dodecahedron). In my implementations I reference this reuse and include a link to the generalized box fold thread.

One clear difference between the results of the two approaches is that where the generalized box fold changes the overall shape of the fractal, shape inversion (usually) does not. Here's a few example images of the exterior of shape inversion Mandelboxen, showing that while the detailed structure does change, the overall shape remains a cube. Images are for standard spherical inversion, cube inversion, octahedral inversion and inversion using a linear blend between sphere and cube.
 

 

And the same set of shape inversions again: sphere, cube, octahedron, sphere/cube blend. But this time a face-on view zoomed into a corner, and with the Fragmentarium raytracer detail setting turned up higher. At this scale the differences compared to standard spherical inversion become clearer.
 

 

One direction I'd really like to explore is using both generalized box fold and shape inversion approaches in one modified Mandelbox algorithm. So that for example one could have the BoxFold use an octahedron for reflections while the SphereFold uses a rounded cube for inversions. Has anyone implemented the generalized box fold in Fragmentarium? I'm already having performance issues with the part I translated to reuse for shape intersections, so I'm not sure how practical this is in Fragmentarium. My GLSL code is extremely unoptimized though  :)

Offline CozyG

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« Reply #5 on: September 10, 2018, 01:49:28 PM »
very cool!

Inspires me to keep working on Fragmentarium ;)

Thanks 3DickUlus! And thanks for the continued work on Fragmentarium! I've recently been making videos using the camera and parameter animation tools, hoping to post a few this week.

Offline CozyG

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« Reply #6 on: September 10, 2018, 02:20:38 PM »
@cozyG, images look great O0

Thanks mclarekin! Planning to post more images to the galleries soon.

@fract tower . Thanks for the Generalized Box Fold in Mandelbulber. 2010 was long time ago,   I only found fractal forums in 2013, so I missed out on the cool development that was happening in those earlier days.

I found fractalforums relatively late too. Though I've been developing fractal and IFS code in JWildfire for 3+ years, and had occasionally stumbled into fractalforums while following fractal links, I didn't really dive in until last year. This is probably a topic for another thread, but one thing I wonder about all that amazing work from previous years -- do any of you involved back then ever think nowadays about publishing some of your work as a more traditional journal article or conference paper? There is still very little published (in the traditional peer-reviewed sense) about the Mandelbox and other fractal graphics developments that have first appeared in fractalforums.

Offline lkmitch

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« Reply #7 on: September 10, 2018, 06:25:02 PM »
I'm excited to share with fractalforums that I recently published a peer-reviewed paper, "Extending Mandelbox Fractals with Shape Inversions", in the proceedings of the Bridges 2018 math/art conference!  The conference was in Stockholm near the end of July, but I've been holding off on posting about this until now so I could also get a slightly modified version up on arXiv.org, and get my github repo presentable.

Congratulations! Now that the conference is over, I guess I can safely say that I was one of your paper's reviewers.  :)

Offline 3DickUlus

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« Reply #8 on: September 10, 2018, 07:12:22 PM »
Thanks 3DickUlus! And thanks for the continued work on Fragmentarium! I've recently been making videos using the camera and parameter animation tools, hoping to post a few this week.

just finding the time to look at improving those interfaces (subject for another thread), if the tutorials fall short please don't hesitate to ask me for input. ;)

Offline pauldelbrot

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« Reply #9 on: September 11, 2018, 12:17:59 AM »
This is probably a topic for another thread, but one thing I wonder about all that amazing work from previous years -- do any of you involved back then ever think nowadays about publishing some of your work as a more traditional journal article or conference paper? There is still very little published (in the traditional peer-reviewed sense) about the Mandelbox and other fractal graphics developments that have first appeared in fractalforums.

Alas, most of us aren't in academia, even those of us with postsecondary degrees, and don't have the necessary access to do those kinds of things.

Offline gerrit

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« Reply #10 on: September 11, 2018, 12:48:02 AM »
Alas, most of us aren't in academia, even those of us with postsecondary degrees, and don't have the necessary access to do those kinds of things.
Anyone can submit a paper. Lot of work though...

Offline pauldelbrot

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« Reply #11 on: September 11, 2018, 01:11:52 AM »
Anyone can submit a paper. Lot of work though...

That might theoretically be true, but it will be expected to have particular formatting and to adhere to particular norms, to cite other papers on the same topic that have previous work that yours built on, and so on and so forth. Where are the people who can edit it to fit those formatting norms, or at least advise you in the matter of making it presentable? In academia. Where must you be to access those earlier papers without paying through the nose? In academia. There's a de facto barrier to entry for anyone not employed on a university campus and it's sky-high.

Offline gerrit

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« Reply #12 on: September 11, 2018, 01:27:39 AM »
That might theoretically be true, but it will be expected to have particular formatting and to adhere to particular norms, to cite other papers on the same topic that have previous work that yours built on, and so on and so forth. Where are the people who can edit it to fit those formatting norms, or at least advise you in the matter of making it presentable? In academia. Where must you be to access those earlier papers without paying through the nose? In academia. There's a de facto barrier to entry for anyone not employed on a university campus and it's sky-high.
Anyone with a post-secondary degree should know how do do all of that and journals provide templates for your favorite work processor (MS Word or Latex).
I'd say 90% of published papers are available for free one way or the other. Problem is that most of the "published" stuff is online, a lot right here, and referring to temporary URL's is usually not acceptable. Main problem is I think a question of motivation. I've considered cleaning up my draft on perturbation theory and related things for a publication, but why should I?

Offline pauldelbrot

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« Reply #13 on: September 11, 2018, 02:00:45 AM »
Anyone with a post-secondary degree should know how do do all of that

Maybe anyone with a master's or Ph.D., but baccalaureates aren't generally taught that bit.

Offline claude

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« Reply #14 on: September 11, 2018, 01:11:30 PM »
The biggest benefit of academic journals is peer review, I suppose, but forums have in-built peer review by their nature, so I don't see all that much of a difference in terms of reputability...  Plenty of nonsense has passed through journal peer review too.  I think it's near-impossible to build a body of journal literature for this fractal art stuff, given that almost all the existing literature is on forums and blogs and is thus not citable due to being "unscholarly", meanwhile simply copying it would be unethical plagiarism.  So we're trapped.

Also, most academic conferences only publish papers that have been presented in person, which requires conference registration, which is expensive, sometimes very expensive, not to mention travel and hotel expenses, etc.  Academics generally have some budget from their institution for attending conferences.


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