Okay. This is my brute force conversion from MatLab to perl, and a simple test harness.:

#! perl -slw
use strict;
use Data::Dump qw[ pp ];
use List::Util qw[ reduce ]; $a = $b;
use GD;
use constant { X => 0, Y=> 1, R => 2 };

sub rgb2n{  unpack 'N', pack 'CCCC', 0, @_ }

my $RED     = rgb2n( 255, 0, 0 );
my $GREEN   = rgb2n( 0, 255, 0 );
my $BLUE    = rgb2n( 0, 0, 255 );
my $YELLOW  = rgb2n( 255, 255, 0 );
my $MAGENTA = rgb2n( 255, 0, 255 );
my $CYAN    = rgb2n( 0, 255, 255 );
my $WHITE   = rgb2n( 255,255,255 );

## Brute force from MatLab code node:1065900
## fx = [0,cumsum(unifrnd(0,1,1,10))];
my @fx = @{ reduce( sub{ push @$a, $a->[-1]+$b; $a }, [ 0 ], map{ 1+ra
+nd 10 } 1..10 ) };

## tmp=unifrnd(1,10,1,1e5);
my @tmp = map{ 1+ rand 10 } 1 .. 1e5;

## ix=floor(tmp);
my @ix = map int, @tmp;

## dx=rem(tmp,1);
my @dx = map $_-int($_), @tmp;

## values = (fx(ix) + (fx(ix+1)-fx(ix)).*dx)./fx(end-1);
my @values = map{
    ( $fx[ $ix[$_] ] + ( $fx[ $ix[$_+1] ] - $fx[ $ix[$_] ] ) * $dx[$_]
+ ) / $fx[-1]
} 0 .. $#ix-1;


our $N //= 100;
our $X = our $Y //= 800;

## pick points from values
my @points = map[ 
    int( $values[ rand @values ]*$X ), int( $values[ rand @values ]*$Y
+ ) 
], 1 .. $N;

my $im = GD::Image->new( 1000, 1000, 1 );
$im->fill( 0, 0, $WHITE );
$im->rectangle( 100, 100, 900, 900, 0 );

$im->filledArc( 100+$_->[X], 100+$_->[Y], 5, 5, 0, 360, $RED ) for @po
+ints;

open PNG, '>:raw', "$0.png" or die $!;
print PNG $im->png;
close PNG;
system "$0.png";
[download]

Does the conversion look right? Am I using the values correctly?

It produces datasets like this which doesn't appear to demonstrate much in the way of clumping. What did I do wrong?

Your translation looks correct, so I'm a bit surprised by the result. I only tested it in 1-D, but the histogram looked plenty spiky. You could make it spikier by raising the random numbers used to generate @fx to some power, but it sounds like you found another solution.

You could make it spikier by raising the random numbers used to generate @fx to some power

Indeed, adding a power component causes much more clumpiness, and making the power component variable:

my @fx = @{ 
    reduce( sub{ push @$a, $a->[-1]+$b; $a }, [ 0 ], map{ rand()**rand
+(3) } 1..10 ) 
};
[download]

gives a nice variability.

But yes, I am currently much enamoured of my weight-map solution. Some of the grey-scale images it produces are just downright beautiful :)

But thankyou for your input. The vectorising of the 3D weight-map to 1D weight-stick my solution uses. came directly from your example, and I understand a little more about matlab/octave now :)

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