This is a multi-part message in MIME format.
--------------000706010009020706010207
Content-Type: text/plain; charset=ISO-8859-1; format=flowed
Content-Transfer-Encoding: 7bit
Craig Markwardt wrote:
>
>
>You probably need a baseline comparison. In other words, would
>simulated gaussian noise with the same power spectrum as the CMB give
>the same fractal dimension results?
>
>CM
>
>
Craig Markwardt,
Wendelin Werner ( recent fields medalist) has done work on
a very similar type of problem
and there are graphics at:
http://www.math.u-psud.fr/~werner/
http://www.math.u-psud.fr/%7Ewerner/pub.html
The area of study is called Brownian islands.
http://swiss.csail.mit.edu/~rauch/islands/
So I'm actually able to answer you for the 2d case
from a Mandelbrot published article on the Internet:
http://www.edge.org/3rd_culture/mandelbrot04/mandelbrot04_index.html
> Empirical measurement yielded 1.3336 and on this basis, my 1982 book,
> /The Fractal Geometry of Nature, /conjectured that the value of 4/3 is
> exact. Mathematician friends chided me: had I told them before
> publi****ng, they could have quickly provided a fully rigorous proof of
> my conjecture. They were wildly overoptimistic, and a proof turned out
> to be extraordinarily elusive. A colleague provided a numerical
> approximation that fitted 4/3 to about 15 decimal places, but an
> actual proof took 18 years and the joining of contributions of three
> very different scientists. It was an enormous sensation in the year
2000.
It was this proof that got Wendelin Werner the Fields Medal
more than anything.
--------------000706010009020706010207
Content-Type: text/html; charset=ISO-8859-1
Content-Transfer-Encoding: 7bit
<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
<html>
<head>
<meta content="text/html;charset=ISO-8859-1" http-equiv="Content-Type">
</head>
<body bgcolor="#ffffff" text="#000000">
Craig Markwardt wrote:
<blockquote cite="midm21wjp1d1g.fsf@[EMAIL PROTECTED]
" type="cite"><br>
<pre wrap=""><!---->
You probably need a baseline comparison. In other words, would
simulated gaussian noise with the same power spectrum as the CMB give
the same fractal dimension results?
CM
</pre>
</blockquote>
Craig Markwardt,<br>
Wendelin Werner ( recent fields medalist) has done work on <br>
a very similar type of problem<br>
and there are graphics at:<br>
<a class="moz-txt-link-freetext"
href="http://www.math.u-psud.fr/~werner/">http://www.math.u-psud.fr/~werner/</a><br>
<a class="moz-txt-link-freetext"
href="http://www.math.u-psud.fr/%7Ewerner/pub.html">http://www.math.u-psud.fr/%7Ewerner/pub.html</a><br>
The area of study is called Brownian islands.<br>
<a class="moz-txt-link-freetext"
href="http://swiss.csail.mit.edu/~rauch/islands/">http://swiss.csail.mit.edu/~rauch/islands/</a><br>
<br>
So I'm actually able to answer you for the 2d case<br>
from a Mandelbrot published article on the Internet:<br>
<a class="moz-txt-link-freetext"
href="http://www.edge.org/3rd_culture/mandelbrot04/mandelbrot04_index.html">http://www.edge.org/3rd_culture/mandelbrot04/mandelbrot04_index.html</a><br>
<blockquote type="cite"><font
face="Verdana, Arial, Helvetica, sans-serif" size="2"> Empirical
measurement yielded 1.3336 and on this basis, my 1982 book, <i>The
Fractal Geometry of Nature, </i>conjectured that the value of 4/3 is
exact. Mathematician friends chided me: had I told them before
publi****ng, they could have quickly provided a fully rigorous proof of
my conjecture. They were wildly overoptimistic, and a proof turned out
to be extraordinarily elusive. A colleague provided a numerical
approximation that fitted 4/3 to about 15 decimal places, but an actual
proof took 18 years and the joining of contributions of three very
different scientists. It was an enormous sensation in the year
2000.</font></blockquote>
It was this proof that got Wendelin Werner the Fields Medal<br>
more than anything.<br>
</body>
</html>
--------------000706010009020706010207--
|
