RIDDLES OF THE SPHINX

Dr. Mitsu Matsu, the world-renowned genetic engineer, was the first to construct two-dimensional life forms. Well, not exactly two dimensional, but almost. They are crystal-like microorganisms that flourish in monolayer cultures, that is, cultures only one molecule thick.

Matsu called his organisms “reptiles” for two reasons: they replicate themselves, and they are shaped like polygonal tiles. All reptiles are much too small to be visible except in powerful neutrino microscopes. They slowly swim about through the mondayer liquid by means of tiny cilia on their borders and obtain food by absorbing it through their “skin.” As a reptile grows, it preserves its polygonal shape. When it reaches a critical size, it splits not in half, like an amoeba, but into four smaller congruent tiles, each similar to the original. The four newly “born” reptiles need not be of the same “handedness” as the original. That is, one or more of the four may be mirror images of the original.

At first, Matsu was able to create reptiles only in the shapes of triangles and squares. It is easy to see how any triangle T can be divided into four smaller triangles, congruent to each other and similar to T, and how parallelograms can be split into four smaller similar parallelograms. Several months later he managed to produce three other reptiles, each with four sides, and three six-sided reptiles. They are shown below.