I think that this is the same basic structure as the tiling of Penrose's hyperbolic tiles decribed by Warren in his penultimate e-mail: http://cp4space.files.wordpress.com/2013/09/bs-tiling.png Does it actually have a name? I've always called it a `Baumslag-Solitar tiling' (c.f. B-S group), but that's certainly non-standard terminology. Warren described it as an `Escher hierarchical tiling', and upon searching it indeed features as the basic structure of Square Limit: http://www.tess-elation.co.uk/self-similar-tessellations It isn't equivalent to any nice tessellation of the Euclidean or hyperbolic plane, since it doesn't have an orbifold. Baumslag-Solitar tilings arise naturally in the complement of the Mandelbrot set, as shown below: http://cp4space.files.wordpress.com/2013/09/bs-mandelbrot.png Indeed, if we have a complex polynomial iteration and the polynomial has degree d, then we get a B-S tiling of order d. Sincerely, Adam P. Goucher http://cp4space.wordpress.com