Here, I will draw the picture using words.

Let \\(f\\) be an arrangement of \\(k\\) subsquares \\(s_1,..s_k\\) within the unit square.

Let \\(w_i\\) be the width of square \\(i\\).

Suppose that we have arrangements \\(g_1,...,g_k\\) which we wish to compose into \\(f\\).

The interpretation of this will be to nest each \\(g_i\\) as a sub-arrangement of \\(f\\), installing it at the site of \\(s_i\\).

\\(s_i\\) will function as a frame for the installation of a scaled-down copies of the subsquares that comprise \\(g_i\\).

In particular, the subsquares of \\(g_i\\) will get scaled down by the factor \\(w_i\\) before being installed into the frame \\(s_i\\).

So now, on our mental 'workbench', we have the unit square, subsquares \\(s_i\\), and sub-subsquares, which have been scaled down.

The final composite is defined by discarding the intermediate subsquares \\(s_i\\), and just retaining the outer unit square and the scaled down sub-subsquares.

Let \\(f\\) be an arrangement of \\(k\\) subsquares \\(s_1,..s_k\\) within the unit square.

Let \\(w_i\\) be the width of square \\(i\\).

Suppose that we have arrangements \\(g_1,...,g_k\\) which we wish to compose into \\(f\\).

The interpretation of this will be to nest each \\(g_i\\) as a sub-arrangement of \\(f\\), installing it at the site of \\(s_i\\).

\\(s_i\\) will function as a frame for the installation of a scaled-down copies of the subsquares that comprise \\(g_i\\).

In particular, the subsquares of \\(g_i\\) will get scaled down by the factor \\(w_i\\) before being installed into the frame \\(s_i\\).

So now, on our mental 'workbench', we have the unit square, subsquares \\(s_i\\), and sub-subsquares, which have been scaled down.

The final composite is defined by discarding the intermediate subsquares \\(s_i\\), and just retaining the outer unit square and the scaled down sub-subsquares.