Harriss Spiral - Make Your Own
Edmund Harriss, mathematician and artist, has come up with a beautiful new fractal spiral, with an elegant ratio analagous to the Golden ratio. What shape would a rectangle be if it divided into two similar rectangles and a square? He then made a beautiful recursive spiral in this structure using quarter circles on the squares.
Read more by Alex Bellos in the Guardian:
http://www.theguardian.com/science/alexs-adventures-in-numberland/2015/jan/13/golden-ratio-beautiful-new-curve-harriss-spiral
You may have to download the sketch to have access to the tools which allow you to build the spiral.
My example: http://www.geogebratube.org/student/m480255
A gif demo: http://mathhombre.tumblr.com/post/108047015734/harriss-spiral-edmund-harriss-mathematician-and