+--+--+--+--+--+--+--+--+--+--+
| 0| 0| 0| 0| 0| 0| 0| 0| 0| 0|
+--+--+--+--+--+--+--+--+--+--+
| 0| 5| 5| 4| 3| 3| 2| 2| 1| 0|
+--+--+--+--+--+--+--+--+--+--+
| 0| 5|10| 8| 6| 5| 4| 3| 1| 0|
+--+--+--+--+--+--+--+--+--+--+
| 0| 3| 6| 5| 5| 5| 5| 4| 2| 0|
+--+--+--+--+--+--+--+--+--+--+
| 0| 1| 2| 3| 4| 5| 6| 6| 3| 0|
+--+--+--+--+--+--+--+--+--+--+
| 0| 0| 1| 2| 3| 5| 5| 4| 3| 0|
+--+--+--+--+--+--+--+--+--+--+
| 0| 0| 0| 1| 2| 4| 3| 3| 2| 0|
+--+--+--+--+--+--+--+--+--+--+
| 0| 0| 0| 0| 1| 2| 1| 2| 1| 0|
+--+--+--+--+--+--+--+--+--+--+
| 0| 0| 0| 0| 0| 0| 0| 0| 0| 0|
+--+--+--+--+--+--+--+--+--+--+

##</code><code>##

([0,0])x 0, ([0,1])x 0, ([0,2])x 0, ...
([0,1])x 0, ([1,1])x 5, ([2,1])x 5, ([3,1])x 4, ([4,1])x 3, ...
([0,2])x 0, ([1,2])x 5, ([2,2])x 10,([3,2])x 8, ...
...

##</code><code>##

#! perl -slw
use strict;
use Data::Dump qw[ pp ]; $Data::Dump::WIDTH = 1000;
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 );

sub gen_rand {
    my $rand_high = shift;

    my $high_part = $rand_high;
    my $rand_sum = 0;

    while ($high_part) {
        my $rand_arg = 1 + int rand $high_part;
        $high_part -= $rand_arg;
        $rand_sum += int rand $rand_arg;
    }
    return $rand_sum;
}

our $N //= 1000;
our $X //= our $Y //= 500;
our $W //= 10;

## Initialise the weight map to zeros.
my @map = map[ ( 0 ) x $X ], 1 .. $Y;

## Pick a random number of random 'peak' points.
my @peaks = map[ int rand $X, int rand $Y ], 1 .. ( 1 + rand( 8 ) );

for my $peak ( @peaks ) {
    ## pick a random value for this peak
    my $val = 2 + int rand $W;

    ## and grade it out to the left edge (if the peak isn't at the left edge)
    if( $peak->[X] > 0 ) {
        my $delta = $val / ( $peak->[X] );
        $map[ $peak->[Y] ][ $_ ] = $map[ $peak->[Y] ][ $_-1 ] + $delta  for 1 .. $peak->[ X ];
    }
    ## and grade it out to the right edge (if the peak isn't at the right edge)
    if( $peak->[X] < $X ) {
        my $delta = $val / ( $X - $peak->[X] );
        $map[ $peak->[Y] ][ $_ ] = $map[ $peak->[Y] ][ $_-1 ] - $delta  for $peak->[ X ]+1 .. $X;
    }
}

## Now grade out between the x-lines and the top and bottom edges.
for my $x ( 0 .. $X-1 ) {
    my $first = 0;
    for my $second ( map( { $map[$_][$x] != 0 ? $_ : ()  } 0 .. $Y-1 ), $Y-1 ) {
        my $delta = ( $map[ $second ][$x] - $map[ $first ][$x] ) / ( $second - $first );
        $map[$_][$x] = $map[$_-1][$x] + $delta for $first+1 .. $second;
        $first = $second;
    }
}

## Draw and display the weight map as grey scale image for visualisation and checking
my $im = GD::Image->new( $X+2*100, $Y+2*100, 1 );
$im->fill( 0, 0, $WHITE );
$im->rectangle( 100, 100, $X+100, $Y+100, 0 );

for my $y ( 0 .. $#map ) {
    for my $x ( 0 .. $#{ $map[0] } ) {
        my $rgb = int( $map[$y][$x] ) * 255 / $W;
        $im->setPixel( 100+$x, 100+$y, rgb2n( ( $rgb ) x 3 ) )
    }
}
open PNG, '>:raw', "$0.png" or die $!;
print PNG $im->png;
close PNG;
system "$0.png";

## Vectorise the weight map to a weight stick
my $stick = '';
for my $y ( 0 .. $#map -1 ) {
    for my $x ( 0 .. $#{ $map[ 0 ] } -1 ) {
        ## The -3 ensures isolated islands of points; but creates an edge case.
        my $packed = pack( 'vv', $x, $y ) x ( $map[ $y ][ $x ] -3 );
        $stick .= $packed;
    }
}

## a sub that uses the weight stick to generate weighted random values.
sub rndPoint {
    my $rnd = int rand( length( $stick ) / 4 );
    my @point = unpack 'vv', substr( $stick, $rnd*4, 4 );
    return \@point;
}

## generate some points
my @points = map rndPoint(), 1 ..$N;

## Draw the points over the weight map for checking
$im->filledArc( 100+$_->[X], 100+$_->[Y], 5, 5, 0, 360, $RED ) for @points;

## and display it.
open PNG, '>:raw', "$0.png" or die $!;
print PNG $im->png;
close PNG;
system "$0.png";