Predicting the limiting radius via extrapolation from Rn(t)

Investigate whether extrapolation from the sequence of radial values Rn(t), computed at fixed t for the iterated rear-track sequence derived from the polar square root spiral, can be used to predict the limiting radial value R∞(t); develop a method that succeeds or demonstrate that such extrapolation is ineffective.

Background

The authors observe numerical convergence of the iterated rear tracks Fn(t) to a limiting spiral and consider whether one could predict the limit radius R∞(t) from the finite sequence of radii Rn(t) at fixed t using extrapolation techniques.

They explicitly report failure to find a working extrapolation method, marking this as an unresolved practical and theoretical question.