Hi Brian!

>>Somehow, the latest ArchimedeanSpirals script is getting away with theta=0.
add line:
if (theta===0) { theta=0.0000001 }

>>The onmousemove slider generates the flashing curves, I would guess from repetitive calculations.
Check the new code (attached)
Use diff tool, or any online tool like http://www.quickdiff.com/

P.S. Thank you for a moi.ui.fireUIEvent command :) I didn't know about it :)