okay now that I'm awake: Yeah, string art is the way to do this, it isn't actually a spirograph in the traditional sense - it's all straight lines between two plotted points that move, vs a spirograph is working in curves lines from the get-go.
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That said, you can get similar looks to the result in the preview by doing gear-outside-gear to produce https://en.wikipedia.org/wiki/Epitrochoid curves rather than the usual hypotrochoids (gear in hoop) - the inner structure will be similar but the outside will come to a smooth circle.
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