Shapes with repetitions

There are two more ways of generating a regular triangle from three pieces.

We call these shapes with three-fold symmetry MitsuMata (三又 in Japanese). A MitsuMata can be constructed from a Lion by changing the way one piece is connected. Similarly, by changing the way one of the connector pieces of a level-n approximation of the Sierpinski tetrahedron is connected, one can generate a subspecies of a Mitsumata.
[Pictures for n = 1, n = 2 to be prepared]
By extending the three connectors of a Mitsumata to Mitsumata's, we have the following shape.
[To be prepared]
By repeating this extension infinitely, one can form the following infinite shape with a repetition pattern.
One can consider its variation:
The above one is generated be extending connectors with Mitsumata's and level-1 subspecies of Mitsumata alternatively.

The following left figure is obtained only with level-1 subspecies of Mitsumata, and the right figure with level-1 and level-2 subspecies of Mitsumata. Note that they consist only of Lions, not Mitsumata.

In this way, one can generate infinitely large shapes with two kinds of subspecies of Mitsumata arranged along sides of triangular holes.

One can generate many other shapes with repetitions, more precisely, shapes with P3 symmetries. The following figure is one example.

[Modify this picture]