A heuristic description of a personal learning experience in a LOGO micro‐world is given. The figures produced by the familiar POLY procedure are generalized, and an attempt is made to develop a workable definition and a useful classification. It depicts the gradual evolution of relevant mathematical concepts, and the part intuition played in this process. Moreover, it shows mathematics both as a process of discovery and creative work, illustrating the difference between the final product and the untidy processes used to arrive there.