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During the past year, we have completed two important steps in our program for understanding the biological and computational significance of patterns of spatial mapping in the brain. First, we have found a simple algorithm which is capable of describing and synthesizing the patterns of ocular dominance columns and orientation columns in the cat and monkey. This algorithm is controlled by a small number of parameters, and we show that it produces patterns which are simular to those in our lab, and elsewhere, obtained from animal experimentation. Moreover, we show that a number of previously published algorithms for simular purposes can be shown to be equivalent to our algorithm. The significance of this work is that we can now describe and synthesize some of the major architectural features of cat and monkey sensory cortex with high accuracy. In addition, we have obtained some insight into the essential simplicity of these patterns. This work is currently in press in Biological Cybernetics. In addition, we have developed an algorithm for pattern recognition based on the multiple, parallel two dimensional mapping of the input data. We view this as an important step in our goal of developing insight into the use of multiple, parallel sensory mappings in the brain. We believe that this algorithm is the first pattern recognition algorithm to make explicit use of the kind of data format which is characteristic of the brain.