Problem solving based on error minimization in cellular systems with phase fields instead of connections

It is explained how a cellular automaton can grow patterns that correspond to trained networks. Since a pattern corresponds to a map between an n-dimensional and an m-dimensional space, such a pattern can be called a 'meta-pattern'. The problems solved by connectionist multi-layered networks can be solved by the automaton too. In addition, it allows for a straightforward representation of patterns with internal bindings, even if such bindings are organized at several, hierarchically related levels. Further, if a problem has symmetry, then the form corresponding to its solution usually is aesthetically attractive. This contrasts with the black-box nature attributed to the classical connectionist approach. Since problems with symmetry are often called 'beautiful problems', the present system gives beautiful solutions for beautiful problems.