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Author Topic: Two further spherical coordinate systems  (Read 3445 times)
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twinbee
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« Reply #15 on: March 25, 2010, 08:22:49 PM »

Since the new year, I haven't done much research into finding the true 3D brot, but it's great to see so much progress by everyone on this front. I'll probably get hooked in again myself at some point. wink

Quote
I would like to know if twinbee tried all the coordinate systems he posted here http://www.physicsforums.com/showthread.php?t=331883, at least the working ones. Are the results somewhere?

I scrapped most of them for various reasons, but my best (though limited) hope now lies with system G. If someone could code that up (if it hasn't been tried already), that'd be awesome.
« Last Edit: March 25, 2010, 08:24:36 PM by twinbee » Logged
Mircode
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« Reply #16 on: March 25, 2010, 10:07:42 PM »


Quote
I scrapped most of them for various reasons, but my best (though limited) hope now lies with system G. If someone could code that up (if it hasn't been tried already), that'd be awesome.

I'm afraid that system G also suffers from this:

Quote
While the lines of a coordinate system may intersect at almost any angle, they may NOT be parallel, because then they cease to distinguish different points. For example, your systems D and B suffer from this on the circle where the sphere intersects the y-z plane.
(physics forums)

Sorry wink
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twinbee
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« Reply #17 on: March 25, 2010, 10:19:07 PM »

Yes, I remember that, although I still have a little hope because the numbers used for that part of the rotation may lead to a singularity 'join' in that part of the fractal (perhaps where two big spheres meet?), so it doesn't matter how the numbers come out. In theory anyway - I might be confused on that.

Any luck trying out the formula for the first pic in this thread? smiley
« Last Edit: March 25, 2010, 10:30:58 PM by twinbee » Logged
Timeroot
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« Reply #18 on: March 26, 2010, 12:21:50 AM »

I know that it doesn't represent the true Mset quite so accurately, but a while back I was considering spherical coordinates, where the radius coordinate actually measured the distance to some off-center point, say (0,1,0) or even (0,0.01,0). This leaves the angles on "coincident circles" determinable. Might be worth a shot, although with something like (0,0.01,0), I think the whipped cream would be taken to a whole new level. Either that, or pole-like "super distortion".  embarrass
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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.
twinbee
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« Reply #19 on: March 26, 2010, 09:34:07 PM »

Sounds like an idea. After some rendering, I think whippy sounds about right wink

I tried also offsetting the rotation origin point too. And with various permuations of numbers (x,y,z for each pic). Oh, small offsets like 0.01 didn't seem interesting (just tiny distortions mostly).

http://www.skytopia.com/project/fractal/new/other/mr-whippy.jpg

Btw, when I tried to post the pic here, Fractal Forums resized the pic to a tiny width (180 pixels). Does anyone know how to avoid the resizing altogether?
« Last Edit: March 26, 2010, 09:39:06 PM by twinbee » Logged
cKleinhuis
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« Reply #20 on: March 26, 2010, 11:20:33 PM »

@twinbee max allowed attachments: 2
you have an extremely high image ... try to make it more rectangular, but attachment sizes are limited, because attachments are lost in space .... after time !
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twinbee
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« Reply #21 on: March 26, 2010, 11:33:39 PM »

It wasn't an attachment to FF though, but a single tall picture link from my own site, so size (pixels and bytes) is theoretically infinite? (within reason cheesy ).
One could post separate pics, but sometimes it's easier to merge them together and upload just that one to save time. If taken separately, they're only small pics - around 600^2. What do you think?

It seemed okay when I posted the 'tall' pic on this thread a couple of months ago btw:
http://www.fractalforums.com/mandelbulb-renderings/higher-iterations/
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cKleinhuis
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« Reply #22 on: March 26, 2010, 11:39:05 PM »

hmm, it was simply too high!
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Timeroot
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« Reply #23 on: March 27, 2010, 12:37:11 AM »

angle offset (0,0,1) looked pretty cool! cheesy Was this was rendered with regular spherical coordinates, or the G system?
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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.
twinbee
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« Reply #24 on: March 27, 2010, 12:47:06 AM »

Quote
Was this was rendered with regular spherical coordinates, or the G system?

Regular.
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Timeroot
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« Reply #25 on: March 27, 2010, 12:49:15 AM »

Oh... the G system is what I think would get really interesting for very small offsets.
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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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