From a quick overview of the code, it doesn't look like a reflection, but the result of your shading algorithm as it progresses along the y axis:

Spot on! Just a pleasing result of a happy accident. I tried something (that couldn't actually work), but the result was the rather pleasing chromium affect complete with semi-random "reflections".

Which seems odd, since the coloring of each point of a turn should be equal for all turns. Or am I missing something?

Because the height of the turns is not mod 256, but the colors are, the interaction between the two produces the variability in the "reflections".

substituting above line with: my $color = ( abs( $newPoint->[A] ) * 256 );

Spot on again. In my current version of the code, that original line is now coded as these two:

            my $color = abs( $newPoint->[A] ) * 256;
            $R and $color =  ( $color + 100 - $newY ) % 256;
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Given /R to turn the "reflections" on or off. I've also added a 'gold plated' option, but that's not particularly successful yet. It is quite difficult to come up with 256 rgb values that form a pleasing spectral continuum from dark to light. The best I've come up with so far is this.