hi
ulam spiral is the prime numbers spiral, you can find info how to draw it in:
Ulam_spiral

each white dot represent a prime number. in the result we will see that the primes have some limited patterns. the following code draw the spiral (a square spiral), 

#!/usr/local/bin/perl 
use strict; 
use Tk; 
my ($order,$pntcycle,$pnts,$b,$num,$p) = (0);
my $lastnumber;
my $NumOfPrimes=0;
my ($i, $colr, $counter);
my($o, $s) = (250, 20); 
my($pi, $x, $y) = (3.1415926, 0, 0);
print "type the maximum number for the prime spiral \n";
my $lastnumber = <>;
print "please wait \n"; 
my $mw = MainWindow->new; 
my $c = $mw->Canvas(-width => 500, -height => 500); 
$c->pack; 
$c->createLine(50, 250, 450, 250); 
$c->createText(10, 250, -fill => 'blue', -text => 'X'); 
$c->createLine(250, 50, 250, 450); 
$c->createText(250, 10, -fill => 'blue', -text => 'Y'); 
OUTER: 
    for ($i= 1; $i <= 250; $i += 1) { 
    $order=$order+1;
    if ($order == 5){$order = 1;}
    $pntcycle = $pntcycle + 1;
    if ($pntcycle == 3)
       {$pntcycle = 1; $pnts = $pnts + 1;}
    $counter=0;
    while ($counter <= $pnts ) {
      $counter++;
      $num = $num + 1;
      if ($num == $lastnumber+1) {last OUTER;}
      
      &is_prime();
      if ($b != 0) {$colr = "white"; $NumOfPrimes = $NumOfPrimes + 1;}
      if ($b == 0) {$colr = "black";}
      
        if ($order == 1) {$x = $x + 1;}
    elsif ($order == 2) {$y = $y - 1;}
    elsif ($order == 3) {$x = $x - 1; }
        elsif ($order == 4) {$y = $y + 1; }

    $c->createText( $x+$o, $y+$o, -fill => "$colr", -text => '.'); 
    
} 
}
MainLoop;

sub is_prime {
    
        $p=0;
        $b=0;
    my $j=0;
    
    my @prime_;
         for($j=1; $j <= $num; $j++)
             {
             if($num % $j==0)
             {
             $prime_[$p] = "$j";
             $p++;
             }
             if ($prime_[1] == $num)
                {
                 $b = 1;
                }
             
             }
  }

[download]
but i have two problems, it is very slow, in my celeron 2 Ghz i draw the points up to 5000 in about 20 seconds. the algorithm for the checking the primality of numbers i have copied it from somewhere in this forum with a small variation.
the other problem is that the final plot appear after the calculation have finished, i can't see the process of drawing dot by dot.

for comparison here is a visual basic 6 code and an executable file to demonstrate the defference:
http://mihd.net/z58lv6
i am using ActivePerl-5.8.8.817-MSWin32-x86
windows xp

In reply to ulam's spiral too slow by orange

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