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Talk:Constrained random points on a circle: Difference between revisions
Talk:Constrained random points on a circle (view source)
Revision as of 13:30, 3 September 2010
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I'm not very good with stats, but I've seen discussions pop up before about different distributions of points. Is uniform vs normal vs (something?) a significant component of the task? How may it be verified with at most 100 points? --[[User:Short Circuit|Michael Mol]] 12:27, 3 September 2010 (UTC)
I guess that if you count the number of points that lie on a line that passes through the center, then the count should not depend on the angle of that line. So it would be wrong to simply pick a uniform-random value of x and then a uniform-random of y at that location, because that would tend to lead to a higher density of points on the left and right sides (look at the maximally dense version above: there are 12 possible values of y at x==0; but only one at x == +/- 15). A common mistake when generating a set of linked random variables is that the distribution depends on the order in which they are generated.
So, take this Perl code:
<pre>
my @bitmap = map { " " x 32 } 0 .. 31;
for (1 .. 100) {
my $x = int rand(31) - 15;
my $max = sqrt( 225-($x*$x) );
my $min = 100-($x*$x);
$min = $min > 0 ? sqrt $min : 0;
my $y = int rand( $max-$min ) + $min;
$y = -$y if rand() < .5;
$x += 15;
$y += 15;
substr( $bitmap[$y], $x, 1, "#" );
}
print "$_\n" for @bitmap;
# # ## # #
# ### # #### #
# #
# # #
# #
# # # ##
# #
# #
# #
# #
# #
# ##
# #
#
# # #
#
#
## #
## ### # # #
## # # # #
# ## ##
### #
# #
</pre>
Here you can see that the number of points that lie on the X axis (y==0) is much smaller than the number that lie on the Y axis (x==0).
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