The steady increase in curvature of the tendril
as it tightens around a support creates a curve
which is roughly equiangular or logarithmic.
Such a curve can be generated mathematically
by dividing isosceles triangles (bisecting a base
angle each time) or rectangles (the remainder
to be similar to the original rectangle) of any
shape -- there is an infinite family of logarithmic
curves of different pitch.