TITLE: Analysis of Transformations in an Escher spiral print
QUESTION [5 upvotes]: I enjoy making tessellations in GeoGebra that have edge alterations, in the style of M C Escher. I recently renoticed a print of his which featured an interesting double spiral tessellation. 

By collecting data in GeoGebra (http://www.geogebratube.org/material/show/id/32449) I became convinced that it's essentially a logarithmic spiral of right isosceles triangles
(The post with those images is immediately after the previous post on my tumblr.)
But I'm having difficulty describing the edge alterations geometrically. Is it dilation of midpoint rotations? I'd be interested in how other people see the spiral or the tessellation transformations.

REPLY [3 votes]: The light and dark blue logarithmic spirals are suitably translated and scaled versions of
$$
r = e^{0.7\theta/(2\pi)}
$$
in polar coordinates $(r, \theta)$.

To confirm the OP's suspicions and MvG's comment, Escher appears to have hand-interpolated near the center. It appears there is no conformal transformation sending the spirals to loxodromes, compare the following image of loxodromes under a Möbius transformation: