$prevdist = 0;

foreach $ydist ( 0..$radius ) {
  # using the formula:
  # xdist*xdist + ydist*ydist = radius*radius
  $newxdist = int(sqrt( $radius*$radius - $ydist*$ydist));

  # Take advantage of symmetry to plot 4 lines at once
  # (for circle outline, draw a line from the previous
  # point to the new one)
  foreach $xdist ($prevdist..$newxdist) {
    $circle{$x_center-$xdist}{$y_center-$ydist}++;
    $circle{$x_center+$xdist}{$y_center-$ydist}++;
    $circle{$x_center-$xdist}{$y_center+$ydist}++;
    $circle{$x_center+$xdist}{$y_center+$ydist}++;
  }

  $prevdist = $newxdist;
}