(Disney Meets Darwin)

Appendix A
The Morphology Scheme for the Articulated Figures

This section explains the morphological schemes for the most complex of the species of articulated figures in the Character Evolution Tool, the Vertebrates. The expression of morphology from the genotype representation was designed to offer a means to generate great variety in the phenotypes. Variations in topological connectivity of limbs and angles in the joints give rise to structures resembling spiders, birds, four-legged mammals, human-like shapes, and a great variety of monsters. In the predecessor to the Vertebrates I had designed a biomorph with an open-ended structure based on a rather idiosyncratic scheme for expression of morphology from the genotype. This was done as an experiment to see if the pressure to achieve locomotion would cause symmetrical structures to emerge from a search space of mostly asymmetrical forms. Many trial runs suggested that the search space was too large for the GA to easily converge on symmetry, and that the representation may not have been designed sufficiently for evolvability - it did not incorporate a "constrained embryology", in which there are few genes yet each gene controls a more powerful feature of the phenotype [Dawkins, 89]. In discussing his own design for a biomorph, Dawkins refers to the emergence of segmentation in animal morphology in the natural world as a watershed event - as a likely increase in evolvability for those animals which chanced upon it. No such structural scheme exists in my previous phenotype design.

After exploring variations on this open-ended biomorph design, I settled on a generalized bilateral-symmetric structure - the Vertebrates - which still allowed for variation, and even occasional asymmetric features, but was characterized by a more realistic embryological scheme - with segmentation. In this biomorph design, a few basic elements are always present: a central body functioning as a backbone, having anywhere from one to four segments, and opposing pairs of limbs (as many as three), each limb having anywhere from one to four segments. Thus, the simplest topology is one body segment with a pair of opposing one-segment limbs. All segment lengths are set to be equal. Figure 1. shows four typical un-evolved anatomies of figures in their default (resting) stances. In some cases, asymmetry can arise. For instance, if the number of body segments is smaller than the number of limb pairs, extra limb pairs grow out from other limbs. This embryological quirk has been kept in the biomorph design, keeping with the idea that features like this might by chance produce useful strategies for locomotion.

A list of effects of the genes for morphology is given below:

number of body segments
pitch angle of joints between body segments
number of opposing limb pairs
pitch angle at the branch point of each limb pair
yaw (or veer) angle at the branch point of each limb pair
changes in pitch angle at the branching angle among consecutive limb pairs
changes in veer angle at the branching angle among consecutive limb pairs
number of segments in a limb
pitch angle of joints between limb segments
veer angle of joints between limb segments



Appendix B
The Motor Control Scheme for the 3D Articulated Figures


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