Tglad
Fractal Molossus
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« on: March 12, 2010, 01:13:46 AM » |
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Inspired by Jesse's incredible giant tarantula nest of a fractal http://www.fractalforums.com/index.php?action=gallery;sa=view;id=1834 I ended up doing some exploring of the scale -1.5 mandelbox. It seems to have an identity crisis, check it out... The corner is like a mandelbulb with bulbs on top of bulbs, but the pattern is like an apollonian gasket or an Indra's pearls fractal Indra's boxes A close up of the top left circle shows a crystal like shape  This area shows a border like a maskit fractal  Looking at the first image again, not only does the shadow of the nearest box resemble a familiar fractal, but check out the little stalks middle right, a quick close up shows them to be trees. |
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« Last Edit: March 12, 2010, 03:57:27 AM by Tglad »
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Timeroot
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« Reply #1 on: March 12, 2010, 02:05:14 AM » |
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Awesome! What typing of Apollonian packing is that? And what's a maskit? A Julia set with c=([-0.75...0.25],0)?
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Someday, man will understand primary theory; how every aspect of our universe has come about. Then we will describe all of physics, build a complete understanding of genetic engineering, catalog all planets, and find intelligent life. And then we'll just puzzle over fractals for eternity.
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jehovajah
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« Reply #2 on: March 12, 2010, 08:41:26 AM » |
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Its like the flat earth the flat earth society has only dreamed of! What a world for adventures and legends. Any Terry Pratchetts out there?
Wonderful colouring and detail. Thanks for this image set.
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May a trochoid of ¥h¶h iteratively entrain your Logos Response transforming into iridescent fractals of orgasmic delight and joy, with kindness, peace and gratitude at all scales within your experience. I beg of you to enrich others as you have been enriched, in vorticose pulsations of extravagance!
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KRAFTWERK
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« Reply #3 on: March 12, 2010, 09:01:47 AM » |
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Beauty box!
Amazing !
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bib
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« Reply #4 on: March 12, 2010, 10:04:16 AM » |
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Neverending beauty, variety and surprises! The shadow looking like a Mset is striking  |
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Between order and disorder reigns a delicious moment. (Paul Valéry)
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Tglad
Fractal Molossus
Posts: 703
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« Reply #5 on: March 13, 2010, 09:04:08 AM » |
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Timeroot- The gasket-like image is from http://www.aleph.se/andart/archives/2005/11/index.html, he calls it Klienian spheres, and a maskit seems to be the name for the Julia at 0.25. Another look at the first image shows little stars on the nearest big face which are like Koch snowflakes, and a line pattern that is like a type of Cantor dust. |
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kram1032
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« Reply #6 on: March 13, 2010, 09:59:22 AM » |
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YAY! Great shapes  I love it when multiple fractals merge into a bigger one It ´somewhat connects them all |
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Timeroot
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« Reply #7 on: March 13, 2010, 07:33:44 PM » |
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Thanks for the link. It seems that, by setting the value K at around .78 (as opposed to the .9 in the picture you provided) one could get an ever closer correlation. This reminds me of the earlier conformal fractals you did on which there were triangular, square, pentagonal, and hexagonal faces. It seems the entire family is prone to multi-personality disorder.  |
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Someday, man will understand primary theory; how every aspect of our universe has come about. Then we will describe all of physics, build a complete understanding of genetic engineering, catalog all planets, and find intelligent life. And then we'll just puzzle over fractals for eternity.
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cKleinhuis
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« Reply #8 on: March 13, 2010, 09:04:31 PM » |
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Timeroot- The gasket-like image is from http://www.aleph.se/andart/archives/2005/11/index.html, he calls it Klienian spheres, and a maskit seems to be the name for the Julia at 0.25. Another look at the first image shows little stars on the nearest big face which are like Koch snowflakes, and a line pattern that is like a type of Cantor dust. lol, kissing fishes on the left middle ?! in the green pic |
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divide and conquer - iterate and rule - chaos is No random!
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Tglad
Fractal Molossus
Posts: 703
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« Reply #9 on: March 15, 2010, 01:20:35 AM » |
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Here's a close up of the first pic, a beautiful fractal shape isn't it, see how the closer zoom is 'purer' and I suppose more specialised  You'd be forgiven for thinking this fractal just mimicks others, but it seems to have plenty of identity of its own... Leprechaun's garden Jupiter moon-life Crazy extra-terrestrial plant life ! |
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cKleinhuis
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« Reply #10 on: March 15, 2010, 02:39:00 AM » |
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i do not get where the shadows come from ! are they cast from the above structure beneath ? then it is clearly wrong in my eyes  but the image is stunning great!  |
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divide and conquer - iterate and rule - chaos is No random!
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reesej2
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« Reply #11 on: March 15, 2010, 03:08:21 AM » |
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Oh, wow, that's fascinating... I wonder if it's possible to explain the variety? Very, very interesting... Do we know of any other fractals with this kind of range?
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kram1032
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« Reply #12 on: March 15, 2010, 03:36:37 PM » |
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Great zooms |
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Tglad
Fractal Molossus
Posts: 703
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« Reply #13 on: March 15, 2010, 11:55:35 PM » |
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Trifox, the shadows are casting down from the cube shapes above, they are correct though, the shapes have a much more circular profile from the light source's diagonal angle. Reesej2, I think we're really breaking new ground here on fractalforums, its what makes it so fun From what I've seen most 3d fractals outside this forum are directly self-similar (like menger sponge) or have random variation (like fractal lightning). The mandel type fractals are interesting because they are a map of julia fractals, so the pattern varies with location. I imagine other scale Mandelboxes have about the same variation, e.g the standard one (scale 2) http://www.fractalforums.com/index.php?action=gallery;su=user;cat=111;u=853A surprise to me is that this -1.5 Mandelbox isn't all that great to look at in other locations, being only -1.5 it is very dense and so the cube faces are flat surfaces. It seems to leave all the stretch to a few places, where it stretches a lot. Yes, surprisingly these conformal/anti-conformal fractals show stretched areas. The julia sets have no stretch at all, but since mandel sets are a map of julias by location the result can appear stretched. This is why the tricorn looks stretched, and is probably why the mandelbrot isn't made of exact circles and cardoids. |
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cKleinhuis
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« Reply #14 on: March 16, 2010, 12:07:32 AM » |
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after staring at it another loooong time, i can support your argument, but it is not really visible that the buld is "round" from the view angle
hmm, just imaging : "what if some 3d fractals have their corresponding julia shapes as shadows"
lol, please do not take it seriously!
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divide and conquer - iterate and rule - chaos is No random!
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March 30, 2009, 04:40:53 AM
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