The inverse curve of the lituus is an Archimedean spiral with 
, which is Fermat's spiral.
Lituus Inverse Curve
See also
Archimedean Spiral, Fermat's Spiral, LituusExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Lituus Inverse Curve." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/LituusInverseCurve.html