You should definitely start your script with

use strict;
use warnings;
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to help you catch misnamed variables.

But the main thing that's going to help you clarify this script is a subroutine or 2.

It looks like you're doing the same work several times, just changing the angle.

Why not wrap that repeated work into a subroutine that takes the angle as an argument and returns the result of $gif->animend?

Then, your mainline will look much simpler:

$data.=buildCircle(0);
$data.=buildCircle($pi/6);
# ....
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