Re: Random spherical troubles

• To: mathgroup at smc.vnet.net
• Subject: [mg25312] Re: [mg25170] Random spherical troubles
• From: Yossi Lonke <jrl16 at po.cwru.edu>
• Date: Tue, 19 Sep 2000 03:45:41 -0400 (EDT)
• Organization: Dept. Mathematics, CWRU
• References: <8pmmhc\$r6a@smc.vnet.net> <8psh4a\$a8v@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Hello,

Take a look at

http://mathworld.wolfram.com/SpherePointPicking.html

where you'll find the answer to your question.

Yossi Lonke

Geoffrey Steeves wrote:

> I just happened upon this post, but I think I have a similar question.
>
> In studying whether a sequence of numbers is random, one can construct
> what is called a Noise
> Sphere(http://mathworld.wolfram.com/NoiseSphere.html).  When I tried this
> out, I got a non-uniform distibution of points concentrated along
> the verticle axis (phi ~= 0) of the sphere.  Initially I thought that this
> was an artifact of my pseudo-random number generator, but I later tried
> this out with "real" random numbers and got the same distribution.
> Looking at the mapping(as it is shown on the web page):
>
> theta = 2 * Pi * Random[]
>
> phi = Pi * Random[]
>
> r = Sqrt[Random[]]
>
> I thought that the problem was with the distribution in phi.  Is this a
> mistake in the map?  Or am I misunderstanding the what a Noise spehere is
> supposed to be?  Thanks for the help!
>
> --
> _______________________________________________________________________________
>              Geoff Steeves // University of Alberta Physics //
>
>                         http://www.ualberta.ca/~gsteeves
> -------------------------------------------------------------------------------

--
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Dr. Yossi Lonke
Mathematics Department
Case Western Reserve University
10900 Euclid Avenue
Cleveland, Ohio 44106
216 368-5423
http://www.cwru.edu/artsci/math/lonke/home.html
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```

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