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Say I wanted to use an old turntable to create a moire effect to mimic Spock's science station monitor...

That YouTube video doesn't answer the full question. To replicate the moire you need to know the specific pattern used, which were almost certainly Pattern No. 4, "Radial lines 5º" from the "Series (A)" Edmund Scientific Co. "Experimenter's Moiré Kit" (scanned here). Spock's display was two of those with the centers offset slightly and one rotating.

From that page:
t's fun to note if both top and bottom layers are off-center, the arc patterns will transition from a "slow & many-arcs" pattern like in Alpha to a "fast & few-arcs" pattern like in Beta, and back again. We actually see this happening in the large moiré display at Spock's bridge station:
 
That YouTube video doesn't answer the full question. To replicate the moire you need to know the specific pattern used, which were almost certainly Pattern No. 4, "Radial lines 5º" from the "Series (A)" Edmund Scientific Co. "Experimenter's Moiré Kit" (scanned here). Spock's display was two of those with the centers offset slightly and one rotating.
I think you meant to link to the overall page and not one specific image.
 
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