Symbolic substitution logic is based on optical pattern transformations. This space-invariant mechanism is shown to be capable of supporting space-variant operations. An optical implementation is proposed. It is based on splitting an image, shifting the split images, superimposing the results, regenerating the superimposed image with an optical logic array, splitting the regenerated image, shifting the resulting images, and superimposing the shifted images. Experimental results are presented. Examples demonstrate how symbolic substitution logic can be used to implement Boolean logic, binary arithmetic, cellular logic, and Turing machines.