Re: Randomly biased, random numbers.

[RichardK]

I think it might be worth trying polar coordinates, so that each new point is a random distance and direction form the last. Then you can tweak your distance distributions to suit your purpose. If you need to restrict the total area, you could wrap the 2d space or just ignore any points that fall outside.

Math::Trig has handy polar conversion functions, so it would be easy to give it a try.

[BrowserUk]

Nice thought. I tried this and several variations on it:

my $start = [ int( rand 500 ), int( rand 500 ) ];
my @points = map{
    my $a = rand( 2*PI );
    my $d = int( rand 500 );
    my $x = $d * cos( $a );
    my $y = $d * sin( $a );
    $x -= 500 while $x > 500;
    $x += 500 while $x < 0;
    $y -= 500 while $y > 500;
    $y += 500 while $y < 0;
    [ $x, $y ];
} 1 .. $N;

Whilst it certainly tends to create clusters, the clusters tend to be (very) evenly distributed, which doesn't trigger the worse case.

[RichardK]

How about using a inverse log distance distribution? Maybe something like this :-

my $d = max_distance * ( 1 - log( rand(1000) ) / log( 1000 ) );

[BrowserUk]

See Re^2: Randomly biased, random numbers. for a similar type of mapping function and why its not suitable.