Here is the crease pattern for Joel Cooper's Whirls tessellation.
This is the CP I used to fold my sample. It is framed as to get 3 full Whirls in a square gridded in 32nds. To fold it with the same repetitions that Joel did (about 13 whirls), you need a hexagon gridded in 64ths, and collapse centered around one whirl.
The CP as shown folds flat. After collapsing, you can curl the loose edges as you wish.
Also note that the blue polygons (parallelograms and triangles) form a flagstone on the backside. This becomes useful to remember should you get lost while collapsing.
Joel's Original Design: www.flickr.com/photos/origamijoel/3226034160/
Front of My Sample: www.flickr.com/photos/8303956@N08/3737207671/
Backlit of My Sample: www.flickr.com/photos/8303956@N08/3738002468/