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Author Topic: orbit trap  (Read 2182 times)
Description: orbit trap
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ericr
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« on: March 11, 2013, 01:11:32 PM »

does orbit trap is possible in M3D like FractalScience Kit for example ?
Thx
ERIC
chaospros is "old" but look sphere tesselation+kleinian group


* choaspro.jpg (23.95 KB, 640x480 - viewed 260 times.)
« Last Edit: March 11, 2013, 01:54:07 PM by ericr » Logged
Alef
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« Reply #1 on: March 15, 2013, 04:16:29 PM »

Cool thing, I never tought, it can be done there. Could you explain, how did you do it in Chaos Pro. Maybe you should explain in Chaos pro section.
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makc
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« Reply #2 on: March 15, 2013, 07:41:23 PM »

not really relevant to m3d but check this out.
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ericr
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« Reply #3 on: March 15, 2013, 11:15:42 PM »

orbit trap is the base for KLeinian group see arXiv.org
in Chaoos pro a new paro do this seen's 2 or 2 days
in 3d it s impossible for the moment but on day ! do you see the like with M3d
for more expication see  http://arxiv.org/pdf/1206.0087.pdf 
or http://arxiv.org/pdf/0707.2427v3.pdf
the 2nd is the most  important
ericr

« Last Edit: March 15, 2013, 11:32:08 PM by ericr » Logged
makc
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« Reply #4 on: March 16, 2013, 04:00:03 AM »

Quote
the 2nd is the most  important
they suck at writing abstracts. not reading it fiery
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ericr
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« Reply #5 on: March 16, 2013, 11:14:26 AM »

I am french and not vrey god at englih but I do it because ist important
inside is the solution of kleinian group 3d
To be easy orbit  trap = set limit =attractor like lorenz's on


* 100349_fractal-kleinian-group-orbit-trap-01.jpg (46.1 KB, 600x600 - viewed 269 times.)
« Last Edit: March 16, 2013, 11:18:38 AM by ericr » Logged
Jesse
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« Reply #6 on: March 16, 2013, 06:52:39 PM »

Maybe not all suggestions belong to m3d, but if so you have to consider that the program has to calculate distance estimates to get use of the formula, that makes many formulas not work unfortunately  sad

For example the neat orbit trap pictures were rendered with a voxel-based renderer, and i think that there don't exist distance estimates for this kind of formulas, if so please correct me.  smiley
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David Makin
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« Reply #7 on: March 16, 2013, 10:33:01 PM »

Hi Jesse - it is possible to get DE estimates for solid based on orbit trap values but AFAIK it's only been done so far by fudging the values individually for each main formula and each orbit trap type.
I think Paul Nylander has rendered some and I allowed the possibility in my formula for UF - it works but is far from optimum and considerably slower than rendering to a DE surface or an iteration surface.

See:

http://makinmagic.deviantart.com/art/Beating-Mandelbrot-125142130
http://makinmagic.deviantart.com/art/Orbit-Trap-Heightfield-128850151
http://makinmagic.deviantart.com/art/Orbit-Trap-Height-Detail-128912127
http://makinmagic.deviantart.com/art/3D-Pickover-Stalks-test-142906488

The first and last rendered relatively quickly so in fact doing this as "normal" 3D fractals is better/easier than doing it in heightfield form - also the only variation from standard DE is essentially to replace the DE calculation with the orbit trap calculation.
« Last Edit: March 16, 2013, 10:35:02 PM by David Makin » Logged

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Jesse
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« Reply #8 on: March 17, 2013, 01:27:14 AM »

Hi David,

... also the only variation from standard DE is essentially to replace the DE calculation with the orbit trap calculation.

 embarrass   it is often more easy than i thought of, lol.

Thanks again, looks like a good additional option to play with...
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ericr
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« Reply #9 on: March 17, 2013, 10:08:35 AM »

 It is possible   to do that ?, it would be great !
ericr
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David Makin
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« Reply #10 on: March 17, 2013, 10:47:24 AM »

Hi David,

 embarrass   it is often more easy than i thought of, lol.

Thanks again, looks like a good additional option to play with...

The tricky part is that AFAIK there is no algebraic method to get a true distance estimate for general orbit traps - and every single type (formula+trap) is quite likely to require different fudging to get an approximately linear distance estimate.
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The meaning and purpose of life is to give life purpose and meaning.

http://www.fractalgallery.co.uk/
"Makin' Magic Music" on Jango
Jesse
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« Reply #11 on: March 17, 2013, 08:05:01 PM »

The tricky part is that AFAIK there is no algebraic method to get a true distance estimate for general orbit traps - and every single type (formula+trap) is quite likely to require different fudging to get an approximately linear distance estimate.

Ok, so its not really that easy and my first tests were also not that promising as i thought of... was not able to get a really working DE from scratch for a standard bulb and the resulting structures were also somewhat disappointing.
Must read a little more on the math to get the points...
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David Makin
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« Reply #12 on: March 18, 2013, 12:10:10 PM »

Ok, so its not really that easy and my first tests were also not that promising as i thought of... was not able to get a really working DE from scratch for a standard bulb and the resulting structures were also somewhat disappointing.
Must read a little more on the math to get the points...

If it helps I didn't check up on any math basically as I didn't think there'd be anything relevant (at least not below phd level) so I rendered using the brute force method - extremely small steps but only a small image (640*480) and had the program store information relating to the change in orbit trap distance values - from that info I worked out the fudge, it worked quite well for the image and animation I posted but the error in estimation is around a magnitude larger than for standard DE so obviously step sizes have to be reduced accordingly - e.g. with analytical DE one can get away with say 0.75*DE on each step, with Buddhi's method around 0.5*DE but to render orbits accurately needs around 0.1*estimate or smaller.

As for structures being disappointing - don't use a simple point trap that will be fairly mundane - try say a trap to line...
« Last Edit: March 18, 2013, 12:12:28 PM by David Makin » Logged

The meaning and purpose of life is to give life purpose and meaning.

http://www.fractalgallery.co.uk/
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makc
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« Reply #13 on: March 18, 2013, 07:11:45 PM »

or menger sponge )
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ericr
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« Reply #14 on: March 23, 2013, 03:17:52 PM »

and now ?
« Last Edit: March 23, 2013, 03:35:21 PM by ericr » Logged
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