Archimedean Spirals
and their Inverted Images

The curves are defined by these equations:
c(t) = (t/tmax)^exponent * [ cos(t, sin(t) ]
Inversion(vec) = (20/norm(vec))^2 * vec

The spirals have monoton curvature functions,
hence their osculating circles are nested.
Each circle crosses the curve tangentially.