Computer faces: the human Lorenz matrix

Realistic Ekman-type faces were generated by a computer program. Twenty primary parameters (muscle tensions and opening factors), each continuous, were used. Non-linear combination of the primary parameters permits the generation of meaningful faces each governed by a single combined parameter (intensity-parameter). Five major meaningful faces were distinguished, "friendliness", "surprise", "disgust", "anger" and "grief". In contrast to the experiments of Ekman, who combined subregions of photographed meaningful faces by hand, mixing can be done in the computer both more easily and, it turns out, more naturally. Mixed facial expressions in an animal were first drawn in matrix form by Lorenz. A consistent interpretation is possible if the linearly superposed displays are assumed to indicate the state of an autonomous optimizer with n linearly independent subfunctionals. An instant display of a vector in n-dimensional space using faces was already proposed by Chernoff. The present faces have the asset that only "natural" parameters are used. This means that no longer only a single point in n-dimensional space can be displayed, but also a meaningful succession of such points--that is, a whole trajectory.