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Non Affine IFSDeep Menger SpongeQuick Quat Mandy
Deep Menger Sponge
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Description: Created using Ultra Fractal.
Just improving my various 3D algorithms before finally creating a set of full raytracer classes for UF.
Looks like just another view of a Menger Sponge ?
Well it is, but the magnification is *1e14 !
I added bailout to a cube rather than a sphere which massively reduced the errors in the calculations so that instead of the accuracy limit for the magnification being around 1e6, it's now around 1e14 i.e. essentially the same limit as the magnification limit for 2D fractals when not using extended precision.
Although the collision test is considerably slower than using a sphere (requires 6 divides per IFS tree iteration !!) it allows the use of a much better way of getting the normals which avoids casting adjacent rays.

Edit: Thanks to Lycium I converted the 6 divides to 3 divides and 3 multiplies - Duh !
Edit 2: Sorry - make that 3 divides and 6 multiplies !!
Stats:
Total Favorities: 0 View Who Favorited
Filesize: 27.46kB
Height: 480 Width: 640
Keywords: menger sponge deep zoom ifs fractal digital algorithmic ultrafractal 
Posted by: David Makin July 28, 2009, 12:38:00 AM

Rating: **** by 1 members.

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Comments (4) rss
Cyclops
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August 31, 2009, 09:30:10 PM
Very cool!
cKleinhuis
Administrator
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formerly known as 'Trifox'


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July 28, 2009, 03:26:51 PM
hello, too bad that you can not admire the zoom level, because everything looks da same ... sad

but anyway, i am right now thinking of a realtime method to render menger sponges, and i am also thinking about making an endless zoom on it ( not really zoom, but it should look like it ) but right now i am stuck in how to implement in on a gfx card, one method would be path tracing, but i do not like that ....

cheers
lycium
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July 28, 2009, 12:13:20 PM
apologies for my terse emails, i was at work wink
David Makin
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July 28, 2009, 02:58:42 AM
After fixing the algorithm as Lycium suggested and adding an optimised option that does a spherical test before doing the cube test I now have the following timings for a *1,000,000 magnification of part of the sponge rendered at 640*480 on my heat impaired P4HT:

Original Spherical bailout (using adjacent raycasting for normals):
Time 3 mins

Cube bailout, normals calculated without extra ray-casting:
Time 1 min 22 secs

Both Bailouts i.e. spherical test first followed by cube test if not bailed out (again without extra ray-casting):
Time: 57 secs

For some fractals the results from plain spherical bailout will be more aesthetically pleasing but the maximum magnification due to inherent mathematical errors is around 1e6 and it's the slowest method.
The combined method produces better "squarey" objects and is *much* faster but again accuracy runs out at around *1e6 magnification.
Pure cube bailout also produces good results for squarey objects and is considerably faster than spherical bailout but slower than the combined method but has the advantage that you can magnify accurately just about as much as you can standard 2D fractals e.g. up to *1e14 in UF without using extra precision.
 

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