Instead of going round the circle, it may be easier to iterate over all values in one direction, i.e. something like:

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

  # Take advantage of symmetry to plot 4 points at once
  # (for circle outline)
  $circle{$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}++;

  # Or to fill up the whole disc...
  foreach $x ( $x_center-$xdist .. $x_center+$xdist ) {
    $circle{$x}{$y_center-$ydist}++;
    $circle{$x}{$y_center+$ydist}++;
  }
}
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Of course this assumes you're dealing with a grid of integers. Right now it also counts every point on the axis twice but that's easy enough to fix.