uberzev
 |
Pretty simple fractal... (it seems)
http://mathworld.wolfram.com/GosperIsland.html http://www.wolframalpha.com/input/?i=Gosper+island http://library.thinkquest.org/26242/full/fm/fm11.html BTW there's some numbers you need... Scaling: 0.377964473 Rotation: 0.0530739038 This is as close as I've gotten...  |
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| Posted: August 19, 2012 3:26 am | ||||||
ThreeDee
 |
So we're looking at this transformation, repeatedly, correct?
(Image made in Illustrator)  |
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| Posted: August 19, 2012 4:53 am | ||||||
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uberzev
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Yup
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| Posted: August 19, 2012 6:06 am | ||||||
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ThreeDee
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Look familiar?
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| Posted: August 19, 2012 7:07 am | ||||||
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ThreeDee
|
That 6-slice rotation gives us some problems. Of course, if we wanted just the outline of the shape, it wouldn't be a problem. But who wouldn't want to stick an image into the tiles?
 |
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| Posted: August 19, 2012 7:11 am | ||||||
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uberzev
|
Nice job. Once again brilliant minds come to the same conclusion.
This effect probably isn't as interesting as the fractal tessellation or hyperbolic tiling but I'm still obsessed with it. |
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| Posted: August 19, 2012 7:49 am | ||||||
SpaceRay
 |
I like it and is well done, although as said it would be better with some colors or textures.
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| Posted: August 19, 2012 9:11 am | ||||||
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uberzev
|
You like everything SR...
 |
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| Posted: August 19, 2012 9:14 am | ||||||
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uberzev
|
I'm thinking we need our rotation map to look something similar to this...
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| Posted: August 19, 2012 9:00 pm | ||||||
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ThreeDee
|
I believe the problem is that the rotation map gets more complex on each iteration. The easier handling is to duplicate the six-hexagon pattern to both sides (depending on the orientation of your rotation map) so when we use the rotation, the pattern copies fill in the blanks instead of transparency. Not the most efficient of approaches, but it should work.
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| Posted: August 20, 2012 2:07 am | ||||||
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ThreeDee
|
5th iteration with the fill-in technique.
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| Posted: August 20, 2012 2:25 am | ||||||
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SpaceRay
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I do not like everything , I like well done, beautiful and quality things as most of the things that you make that for me are really good, curious and interesting, and I do not like all filters at all. |
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| Posted: August 20, 2012 2:34 am | ||||||
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ThreeDee
|
I got it working up to 8th iteration. At these render sizes you don't see much difference after the 6th.
(8 iterations + antialiasing + old laptop = slow bullet) Unless my computer blows up before it, I'll post 7th iteration with 9x9 antialiasing. I mean it literally: This old laptop overheats and shuts itself off if I run it close to 100% CPU for any extended periods. |
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| Posted: August 20, 2012 2:59 am | ||||||
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uberzev
|
Nice work ThreeDee but there aren't supposed to be holes.
 |
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| Posted: August 20, 2012 3:22 am | ||||||
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ThreeDee
|
7th iteration. (I tossed the outlines.)
Looks like lace to me. What could be really cool looking is if one were to modify this into a height map so that the black portions (expect for the outside) were high, white low, and the resulting "tower" height was proportional to their size. Then make it a displacement map in a 3D program. Perhaps I'll try that...  |
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| Posted: August 20, 2012 3:23 am | ||||||
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ThreeDee
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I think it looks way more interesting with holes. |
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| Posted: August 20, 2012 3:24 am | ||||||
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ThreeDee
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This is one of those fractals that you could do one of those hypnotic infinite zoom animations with.
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| Posted: August 20, 2012 3:26 am | ||||||
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SpaceRay
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What would be good is to see this fractal enlarged and zoomed in to see it better.
I think also that it looks much more interesting with holes |
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| Posted: August 23, 2012 1:49 am | ||||||
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