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Science Forum Index » Fractals Science Forum » area of multibrot-sets
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Message |
| Bruce Wayne |
 Posted: Mon Jan 14, 2008 11:43 am |
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Guest
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Are there any good estimates for the area of multibrot-sets (eg. z->z^5
+c)?
I'm doing a bit of research on that matter but found nothing up to now.
Currently I'm pixel-counting it myself but the values are far from being
precise.
Are there even estimates for the area of sets like z->z^-n+c? In this
case I think it would be more appropiate to count the escaping pixels but
my own efforts lead to very small values not anymore in the precision of
my program. |
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| Roger Bagula |
| Posted: Wed Jan 16, 2008 5:29 pm |
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Guest
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Bruce Wayne wrote:
Quote: Are there any good estimates for the area of multibrot-sets (eg. z->z^5
+c)?
I'm doing a bit of research on that matter but found nothing up to now.
Currently I'm pixel-counting it myself but the values are far from being
precise.
Are there even estimates for the area of sets like z->z^-n+c? In this
case I think it would be more appropiate to count the escaping pixels but
my own efforts lead to very small values not anymore in the precision of
my program.
Here's a link to one of the classic papers on the Mandelbrot set area: (
Yuval Fisher
is known for his work on a fractal compress algorithm for the Department
of the Navy)
Here are upper and lower bounds methods:
http://inls.ucsd.edu/~fisher/Complex/
http://inls.ucsd.edu/~fisher/Complex/area.ps.Z |
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| Bruce Wayne |
| Posted: Mon Jan 21, 2008 11:09 am |
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Thanks, didn't know that one.
It's not exactly what I wanted but certainly is interesting. We'll see if
this algorithm is any help for my problem but I think so. |
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| Guest |
| Posted: Thu Jan 24, 2008 2:40 am |
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On Jan 14, 4:43 pm, Bruce Wayne <enyaw_ec...@gmx.net> wrote:
Quote: Are there any good estimates for the area of multibrot-sets (eg. z->z^5
+c)?
I'm doing a bit of research on that matter but found nothing up to now.
Currently I'm pixel-counting it myself but the values are far from being
precise.
Are there even estimates for the area of sets like z->z^-n+c? In this
case I think it would be more appropiate to count the escaping pixels but
my own efforts lead to very small values not anymore in the precision of
my program.
Some realted work I did, up to where my time allowed my to go:
http://rgba.scenesp.org/iq/fractals/research/msets.pdf |
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| Bruce Wayne |
| Posted: Tue Jan 29, 2008 6:20 pm |
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Guest
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Thanks! Especially your pixelcounting-speedup was a great help.
I got nearly the same values for the area for k>0, no surprise there. But
the M-Sets for k<0 are quite "fuzzy" so the pixelcounted area differs
quite a bit. I'm currently thinking of a way to get more definite
results... |
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