This particular heptiamond can produce an unlimited array of interesting patterns.

Furthermore, by placing three in a particular arrangement, a new shape emerges (currently unnamed).

However, there were a couple of angles that I could not determine, so I asked the help of Michael Dowle who very kindly came up with the answers.

Drawing by Michael Dowle

Disappointingly, initial experimentation with the new shape, didn’t seem to work for radial/chaotic tiling. As you can see below, the shape (highlighted in green), doesn’t quite fit in two of the examples and the other is miles out!

Curiously though and to my surprise, I have since discovered many ways that the new shape can tile, seemingly very chaotically. Results of this coming soon…