I would like to find an expression of a spiral which gets straight at infinity, as in the image below:
so that I can make a parametric plot.
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One natural approach is a polar graph $r = f(\theta)$ with a "first-order" asymptote, such as $f(\theta) = (1/\theta) + e^{-\theta}$ for $\theta < 0$. – Andrew D. Hwang Oct 28 '22 at 16:18
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I feel confident that there's a positive answer to your question, but am unable to access my references due to their still being boxed up from a recent move. However, a previous answer I gave contains these titles: https://math.stackexchange.com/questions/3117027/if-there-are-any-curve-databases-with-structured-data/3117754#3117754, – Cye Waldman Oct 28 '22 at 22:17