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.