For example, let \$$f: \square \rightarrow \square_1,\square_2\$$ be the arrangement consisting of the lower left and upper right quarters of the unit square.

The consider the morphism tree consisting of \$$f\$$ at the root, with two children that are also \$$f\$$.

The composite of this tree (diagram) will be the first iteration of recursively nesting \$$f\$$ within itself.

Specifically, it consists of four subsquares, each of length \$$0.25\$$, arranged along the diagonal from the lower left to the upper right corners of the unit square.