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new 3d form of mandelbrot discovered


kaini

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presently rendering a 100 megapixel mandelbox (10,000 x 10,000) for the purposes of making a big, big (hardcopy) picture

the detail is fucking incredible

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new beta of the sw i use out. it is much faster and has funky new light and shadow effects:

SuperCubeScale2Start_nu.png

i could actually imagine real-time exploration, within limits, within a year;

loads of people are optimising the hell out of the maths on this now.

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and finally a focus on the rosebud

 

yes! glad to have something with organic properties that is a bit different to the regular power8 bulb to mess with.

post-106-127112468729_thumb.jpg

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attached - 2 greyscale pdfs - (both 7x5 A4 pages i thin. designed to be made into a big ass picture, obv.)

 

the 'pixel size' in the first is 5mm, the second 3mm

i feel the much bigger one is definitely the better of the two (duuuh)

boneyardv3.pdf

100mpx.pdf

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it's meant to be pasted together collage-like. it's a 7x5 grid of A4 landscape pages. designed to look good from a distance, even though the 'pixels' are big. bar paying a fucking fortune to a professional printer, i can't think of a better way to get this stuff into a large format.

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I love reading these guys work through these things: http://www.fractalforums.com/3d-fractal-generation/the-mandelbox-is-tenuous/

 

To be honest just looking at the transforms that make up the Mandelbox formula I would expect it to be made up of Cantor Dust.

As to the appearance of renders using my formula but with a high "min. iterations" value, I think the result is more of an issue of very small points being missed by the render - i.e. it is Cantor Dust but there should be a lot more of it.

 

this guy is on the ball, i've seen cantor-dust-like phenomenon all over the place inside the mandelbox

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thank you kaini, that was fantastic! I really think the invention/discovery of mandelbulb/box should be on the top of everyone's year end list, before assange and facebook and whatnot (though I can't remember if it was last year, lol).

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In the future I may pay you to make a music video like that for me. loved it!

 

or make you an offer at least...

 

you would not be the first person ;) unless you're willing to donate a computing cluster, not happening.

but i CAN point you in the direction of people who could do this for you :braindance:

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i love the fact that with most other natural patterns - fractal broccoli, the golden ratio - people go "ooh, what symmetry, what proportion, how harmonious!" But with this all you can say is "omfg cthulu's infinite ass aaaaagh!" So otherworldly.

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yep. it blows my mind that this has always been there. people have hacked through jungles to find ancient temples... and all the while there's been crazy temples waiting for them within a bunch of relatively simple iterative transformations.

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exactly. I'm even more impressed now that people seem to be able to tweak the formulas to switch between "hard" box shapes and bulb shapes at will...it really seems to me there should be some practical application to all this besides the pretty pictures...like we should be able to use these formulas to bend space and time and create warp drive or something...

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exactly. I'm even more impressed now that people seem to be able to tweak the formulas to switch between "hard" box shapes and bulb shapes at will...

 

this sacrifices the mathematical purity of the original mandelbulb equation though. arguably only the original has any theoretical worth, and even that involves some fudging (because 2-d (complex) and 4-d (quaternion) number systems are quite developed, but surprisingly 3-d ones are not). not complaining though!

 

machinery_of_nature_by_richardpfeynman-d325t4e.png

this has a mandelbox transform (in itself a mutant mandelbulb transform) followed by a menger sponge transform, which is a much older branch of fractal maths

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