This work introduces a numerical, continuous measure of symmetry for 3D stick creatures and solid 3D objects. Background information about the property of symmetry is provided, and motivations for developing a symmetry measure are described. Three approaches are mentioned, and two of them are presented in detail using formal mathematical language. The best approach is used to sort a set of creatures according to their symmetry. Experiments with a mixed set of 84 individuals originating from both human design and evolution are performed to examine symmetry within these two sources, and to determine if human designers and evolutionary processes prefer symmetry or asymmetry.

We analyze the effect of different genetic encodings used for evolving three-dimensional agents with physical morphologies. The complex phenotypes used in such systems often require nontrivial encodings. Different encodings used in Framsticks—a system for evolving three-dimensional agents—are presented. These include a low-level direct mapping and two higher-level encodings: one recurrent and one developmental. Quantitative results are presented from three simple optimization tasks (passive height, active height, and locomotion speed). The low-level encoding produced solutions of lower fitness than the two higher-level encodings under similar conditions. Results from recurrent and developmental encodings had similar fitness values but displayed qualitative differences. Desirable advantages and some drawbacks of more complex encodings are established.