At growth = 0.166 (also near 0.122, 0.276) the spiral is an autoevolute in the sense of W.Wunderlich, i.e. the centers of the osculating circles lie on the spiral.Logarithmic_Spiral.pdf
Relations to ODEs: The tangent vectors to the osculating circles define a vector field on the plane outside the origin. The circles and the spiral are integral curves of this vector field, so that uniqueness of ODE solutions fails. Hence: this vector field is not Lipschitz continous.