Combinatorial and Computational aspects of Tilings

“If you don’t see ribbons when you look at figure 5.18 (a rhomb tiling), what do you see? De Bruijn see stacks; physicists have seen rails, trails, tracks and rows.”

M. Senechal Quasicrystals and Geometry CUP 1995

The most important objects for animals are other living things. Viewed as physical objects, animals have relatively few degrees of freedom so that the changing positions of only a few variables suffice for recognition of biological movement. The visual system represents the different dimensions of objects in multiple topographic maps. With the right balance of strengths of excitatory input connections and inhibitory lateral connections neural activity in the maps can persist over many seconds. In the context of this approach to seeing, memory for objects emerges straightforwardly as a persistent neural activity that is spatially localized. Perceptually multistable tilings are particularly useful stimuli for probing the visual mechanism because their constantly changing appearance can be used to capture attention over long periods of time. The results of computational modelling and eye movement recordings obtained with such stimuli reveal how the visual appearance of objects is built up.