Two patchwork blocks, Monkey Wrench and Snail’s Trail, share a construction method that alternates between the two.
Both begin with a 4-patch block:

A square cut diagonally produces two half-square triangles. Sew four half-square triangles to the sides of the 4-patch block. The 4-patch block rotates and stands on-point. This block is called Monkey Wrench:

Sew a round of half-square triangles to the sides of the Monkey Wrench block. The 4-patch block rotates and sits flat. This block is called Snail’s Trail:

Sew a round of half-square triangles to the sides of the Snail’s Trail block and produce another Monkey Wrench block:

Sew a round of half-square triangles to the sides of the Monkey Wrench block and produce another Snail’s Trail block:

The two blocks can build on each other indefinitely. They are limited only by the size of the initial 4-patch block (each round of half-square triangles requires a smaller 4-patch block than the block before).




Notice anything? For each round of half-square triangles, the arms spiral further inward.
When four of these blocks rotate around one corner they produce unique blocks that appear organic when placed next to each other.

When four half-size blocks are superimposed on a full-size block, an interesting thing happens. The resulting blocks can be displayed three different ways: as a half-size pattern only; as a full-size pattern only; or as a combination of the two, with the smaller motif centered on the larger one (I omitted the smaller motif that centers where the larger ones come together).

I will do more with this . . .
I love this! It’s so interesting to see the tessellations embedded within the tessellations. So much potential from such a simple shape. Thanks for sharing.