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I found these curve lists:

But they aren't very structured. Wondering if there is anything with on the order of thousands of highly structured curves.

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  • $\begingroup$ Please define in your question what you mean by "structured curves" and why the curve lists you mentioned fail according to your definition. $\endgroup$ – Somos Feb 18 at 4:42
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I'm assuming that by structured, you mean listed in categories of similar types. My standard references in that regard are

A Catalog of Special Plane Curves, J. Dennis Lawrence, Dover, 1972

CRC Standard Curves and Surfaces, David von Seggern, CRC Press, 1993.

And some auxiliary references

Gnomon: from Pharoahs to fractals, Michael J. Gazal$\acute{\text{e}}$, Princeton University Press, 1999

Spiral: from Theodorus to Chaos, Philip J. Davis, A.K. Peters, Ltd., 1993.

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