Here are some variations on the picture using divisions of 12:

Divisions of 3 are carried out through several generations. Each one is subdivided by 2, also through several generations. The result is 3 equal non-selfsimilar thirds. The opposite of the above scheme: divisions of 2 are carried out, each generation being subdivided by 3. The result is 2 equal non-selfsimilar halves.
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The sum of the two above schemes. The shape is not self-similar.