Unfortunately, it turns out that the Bresenham algorithm isn't exactly the right thing - or I've misconscrewed something. Here's my implementation of it, with extra code to detect the crossings; it does a reasonable distribution of the two arrays, but doesn't quite follow the rules that I originally stated: 

#!/usr/bin/perl -w
# Created by Ben Okopnik on Wed Jul  4 13:39:28 EDT 2007

# Modified and converted to code from Wikipedia entry for "Bresenham"
sub brezzie {
    my ($x1, $y1) = @_;
    ($x1, $y1) = ($y1, $x1) if $y1 > $x1;

    my ($deltax, $deltay) = ($x1, $y1);
    my $error = -$deltax / 2;

    my $y = 0;
    my ($last_a, $last_b) = (0, 0);

    for my $x (0 .. $x1){
        # print $steep ? "$y $x\n" : "$x $y\n";
        if ($y1 > $x1){ 
            ($b, $a) = ($x, $y);
        }
        else {
            ($a, $b) = ($y, $x);
        }

        print "A" if $a > $last_a;
        print "B" if $b > $last_b;

        ($last_a, $last_b) = ($a, $b);

        $error += $deltay;

        if ($error > 0){
            $y = $y + 1;
            $error -= $deltax;
        }
    }
}

brezzie(4, 14);

[download]

Running this results in 'BABBBBABBBABBBBABB' - and what I'm looking for is more like 'ABBBBBABBBBABBBBBA'. Max distance is not quite the same thing as a fair distribution.

I really appreciate the help that you've given me so far!

In reply to Re^2: Spreading out the elements by oko1
in thread Spreading out the elements by Anonymous Monk

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