very nice, thanks for the code and for the patience Marshall
I noticed your code get some Use of uninitialized value in join or string if the circle goes outside of the AoA for high values of row.
I fixed it with a condition more in the nested for loop:
$aoa[$x][$y] = 'x' if ( (($x-$circle_x)**2 + ($y-$circle_y)**2 <= ($ci
# and $x >=0 and $y >=0 )
and $x >=0 and $y >=0 and $x <= $max )
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Reinvent the wheel, then learn The Wheel; may be one day you reinvent one of THE WHEELS.
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