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A cellular method for the solution of function approximation and classification problems is introduced. It solves problems of the type solved by connectionist networks, but has an advantage of visualization. Solutions of complex, high-dimensional and non-linear problems correspond to sets of units that define fractal, two-dimensional patterns of aesthetic attractiveness. These sets, in turn, can be considered as patterns, and stored with a classic connectionist learning rule in a network. Then, one obtains a network in which the memorized patterns correspond to meta-patterns in the sense that they correspond to mappings between input and output patterns. Fractals 2000.08:7-14. Downloaded from www.worldscientific.com by YALE UNIVERSITY on 07/11/15. For personal use only. Fractals 2000.08:7-14. Downloaded from www.worldscientific.com by YALE UNIVERSITY on 07/11/15. For personal use only.

An algorithm for the visualization of n-dimensional binary spaces is considered. The algorithm is put in metric terms, and reformulated in terms of branching structures. The difference between metric and structural visualizations is discussed. Then, a hybrid method is proposed. Tree structures are grown in accordance with a metric error function. The method is illustrated with an example in the context of microbial taxonomy, and compared with a Kohonen map.

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