3D Mandelbrot !

P
Posted By
Penang
Nov 14, 2009
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2014
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16
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Wonder how a 3D Mandelbrot looks like?

http://www.skytopia.com/project/fractal/mandelbulb.html

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PU
Photoshop User
Nov 14, 2009
"Penang" wrote in message
Wonder how a 3D Mandelbrot looks like?

http://www.skytopia.com/project/fractal/mandelbulb.html

beautiful
AB
Alan Browne
Nov 15, 2009
Kabuki wrote:
"Penang" wrote in message
Wonder how a 3D Mandelbrot looks like?

http://www.skytopia.com/project/fractal/mandelbulb.html

beautiful

Cool, indeed. Here are more:

http://www.bugman123.com/Hypercomplex/index.html

I don’t believe these satisfy the self-similar aspect of the Mandlebrot set. For that matter, does such exist in nature?
SB
Sjouke Burry
Nov 15, 2009
Penang wrote:
Wonder how a 3D Mandelbrot looks like?

No, I know!!
DM
David Makin
Nov 15, 2009
On 15 Nov, 00:17, Alan Browne
wrote:
Kabuki wrote:
"Penang" wrote in message
Wonder how a 3D Mandelbrot looks like?

http://www.skytopia.com/project/fractal/mandelbulb.html

beautiful

Cool, indeed.  Here are more:

http://www.bugman123.com/Hypercomplex/index.html

I don’t believe these satisfy the self-similar aspect of the Mandlebrot set.  For that matter, does such exist in nature?

They are most definitely self-similar but they do appear to be missing certain aspects of the classic Mandelbrot such as the antennae. To easily see the self-similarity they exhibit just zoom into say the degree 8 or 9 version and you’ll immediately find that the brocolli "buds" extend to all depths in the normal self-similar manner. For example here’s the deepest zoom I’ve done so far (about as far as you can go without extending precision beyond "double"): http://www.fractalforums.com/gallery/?sa=view;id=1043
RB
Roger Bagula
Nov 15, 2009
On Nov 15, 4:36 am, David Makin wrote:
On 15 Nov, 00:17, Alan Browne
wrote:

Kabuki wrote:
"Penang" wrote in message
Wonder how a 3D Mandelbrot looks like?

http://www.skytopia.com/project/fractal/mandelbulb.html

beautiful

Cool, indeed.  Here are more:

http://www.bugman123.com/Hypercomplex/index.html

I don’t believe these satisfy the self-similar aspect of the Mandlebrot set.  For that matter, does such exist in nature?

They are most definitely self-similar but they do appear to be missing certain aspects of the classic Mandelbrot such as the antennae. To easily see the self-similarity they exhibit just zoom into say the degree 8 or 9 version and you’ll immediately find that the brocolli "buds" extend to all depths in the normal self-similar manner. For example here’s the deepest zoom I’ve done so far (about as far as you can go without extending precision beyond "double"):http://www.fractalforums.com/gallery/?sa=view;id=1043

One of the problems with the cubic Julia version of the 2d Mandelbrot set
is the lack of the rational antenna that characterize the quadratic 2d Mandelbrot set.
These antenna seem to be based on mode locking to rational Farey tree angles.
The broccoli shape of this new 3d Mandelbrot is kind of pretty, but reminds one of a standing wave type of 3d surface
more than a Mandelbrot set.
I don’t think the question is through yet/solved.

But I think the efforts are very pretty fractals.

A symmetrical Mandelbrot is obtained in 2d that retains the antenna feature:
x’=2*x*y-x^2+x0;
y’=2*x*y-y^2+y0
http://www.flickr.com/photos/fractalmusic/4106023768/
This suggests that a symmetrical version something like: x’=2*t*x – x^2 +x0
y’=2*t*y – y^2 +y0
z’=2*t*z – z^2 +z0
Where t symmetrically cycles through {x,y,z} as:
x’=2*y*x – x^2 +x0
y’=2*z*y – y^2 +y0
z’=2*x*z – z^2 +z0
There is no guarantee that this will
preserve the antenna effect,
but it seems worth a try.

Respectfully, Roger L. Bagula

11759 Waterhill Road, Lakeside,Ca 92040-2905,tel: 619-5610814 : http://www.google.com/profiles/Roger.Bagula
alternative email:
D
Dave
Nov 15, 2009
On Sun, 15 Nov 2009 02:19:58 +0100, Sjouke Burry
wrote:

Penang wrote:
Wonder how a 3D Mandelbrot looks like?

No, I know!!

or
Now, I know!!
SB
Sjouke Burry
Nov 15, 2009
Dave wrote:
On Sun, 15 Nov 2009 02:19:58 +0100, Sjouke Burry
wrote:

Penang wrote:
Wonder how a 3D Mandelbrot looks like?
No, I know!!

or
Now, I know!!
Now,now, it was really NO.
AB
Alan Browne
Nov 15, 2009
David Makin wrote:
On 15 Nov, 00:17, Alan Browne
wrote:
Kabuki wrote:
"Penang" wrote in message
Wonder how a 3D Mandelbrot looks like?
http://www.skytopia.com/project/fractal/mandelbulb.html
beautiful
Cool, indeed. Here are more:

http://www.bugman123.com/Hypercomplex/index.html

I don’t believe these satisfy the self-similar aspect of the Mandlebrot set. For that matter, does such exist in nature?

They are most definitely self-similar but they do appear to be missing certain aspects of the classic Mandelbrot such as the antennae. To easily see the self-similarity they exhibit just zoom into say the degree 8 or 9 version and you’ll immediately find that the brocolli "buds" extend to all depths in the normal self-similar manner. For example here’s the deepest zoom I’ve done so far (about as far as you can go without extending precision beyond "double"): http://www.fractalforums.com/gallery/?sa=view;id=1043

I’ll take your word for it. I would need an app to explore this with and I don’t want to install such. Other fish to fry.
HD
Henk de Jong
Nov 15, 2009
On 15-11-2009 2:19, Sjouke Burry wrote:
Penang wrote:
Wonder how a 3D Mandelbrot looks like?

No, I know!!

Still computing Mandelbrot graphics on an Acorn computer? 😉


Met vriendelijke groet,
Henk de Jong
The Netherlands

http://www.hsdejong.nl
Nepal and Myanmar (Burma) – Photo Galleries
SB
Sjouke Burry
Nov 15, 2009
Henk de Jong wrote:
On 15-11-2009 2:19, Sjouke Burry wrote:
Penang wrote:
Wonder how a 3D Mandelbrot looks like?
No, I know!!

Still computing Mandelbrot graphics on an Acorn computer? 😉
I switched to an arc310 and a pentium 🙂

I did program 2 3d mandelbroot movies on the arc 310

Not for general use, just a binary frame dump and a player program to view it.
P
Penang
Nov 16, 2009
On Nov 14, 12:17 pm, Alan Browne
wrote:
Kabuki wrote:
"Penang" wrote in message
Wonder how a 3D Mandelbrot looks like?

http://www.skytopia.com/project/fractal/mandelbulb.html

beautiful

Cool, indeed.  Here are more:

http://www.bugman123.com/Hypercomplex/index.html

I don’t believe these satisfy the self-similar aspect of the Mandlebrot set.  For that matter, does such exist in nature?

The other day I watch an old episode of Discovery, where they talk about the Sun (Sun spots and all that).

The more I look at the waves and bursts from the Sun, the more they look like the 3D Mandelbrots.
MA
Mohamed Al-Dabbagh
Dec 4, 2009
On Nov 14, 7:59 am, Penang wrote:
Wonder how a 3D Mandelbrot looks like?

http://www.skytopia.com/project/fractal/mandelbulb.html

Thank you for that post. For the first time I see the rendering of fractal images. It’s just amazing.

Mohamed Al-Dabbagh
MA
Mohamed Al-Dabbagh
Feb 9, 2010
On Jan 17, 5:55 am, Penang wrote:
Just found couple of stunning pics of the 3D Mandelbulbs
http://fc08.deviantart.net/fs70/i/2010/008/2/3/Mandelbulb_Sp ine_by_ds…http://fc07.deviantart.net/fs51/i/2009/321/0/c/H oneycomb_Heaven_by_ds…http://fc02.deviantart.net/fs50/i/20 09/321/9/9/Mandelbulb_Garden_by_d…http://fc01.deviantart.n et/fs70/i/2010/007/8/a/The_Mandelbulb_by_dspw…http://fc09. deviantart.net/fs71/f/2010/001/6/b/Mandelbulb_Xmas_Treeho… http://fc07.deviantart.net/fs70/i/2010/008/3/f/Hell_Just_Fro ze_Over_b…http://dspwhite.deviantart.com/art/The-Eternal-D ream-149572608http://www.skytopia.com/project/fractal/new/fu ll/Power8side-q20b.jpg

Wow.. They are really breathtaking. It would be even more amazing to incorporate these patterns in an animation with a fly-through camera. It would give impressions of a microscopic treck inside the guts! Yuk! But that would be wonderfull. I liked the christmas tree very much with these added lights to it. Soooooo creative. I would call the garden you show as the MandelBrochli. LOL.
Thank you Penang.

Mohamed Al-Dabbagh
Senior Graphic Designer
E
Ejay
Feb 11, 2010
"Mohamed Al-Dabbagh" wrote in message
On Jan 17, 5:55 am, Penang wrote:
Just found couple of stunning pics of the 3D Mandelbulbs
http://fc08.deviantart.net/fs70/i/2010/008/2/3/Mandelbulb_Sp ine_by_ds…http://fc07.deviantart.net/fs51/i/2009/321/0/c/H oneycomb_Heaven_by_ds…http://fc02.deviantart.net/fs50/i/20 09/321/9/9/Mandelbulb_Garden_by_d…http://fc01.deviantart.n et/fs70/i/2010/007/8/a/The_Mandelbulb_by_dspw…http://fc09. deviantart.net/fs71/f/2010/001/6/b/Mandelbulb_Xmas_Treeho… http://fc07.deviantart.net/fs70/i/2010/008/3/f/Hell_Just_Fro ze_Over_b…http://dspwhite.deviantart.com/art/The-Eternal-D ream-149572608http://www.skytopia.com/project/fractal/new/fu ll/Power8side-q20b.jpg

Wow.. They are really breathtaking. It would be even more amazing to incorporate these patterns in an animation with a fly-through camera. It would give impressions of a microscopic treck inside the guts! Yuk! But that would be wonderfull. I liked the christmas tree very much with these added lights to it. Soooooo creative. I would call the garden you show as the MandelBrochli. LOL.
Thank you Penang.

Mohamed Al-Dabbagh
Senior Graphic Designer

That laink came up as 404 site not found with a link redirecting you. It was blocked by Norton as unsafe with three computer
threats

Ejay

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