Memristors have been utilized as an unconventional computational substrate and gained interest as a medium to implement neuromorphic computations. A mathematical model that also proved its potential is Learning Cellular Automata, that is an amalgam of Cellular Automata and Learning Automata. The realization of the common characteristics of memristive circuits and Learning Cellular Automata can only lead to their combination. Namely, both manage to blend storage and processing capabilities in their basic entity. This study involves the definition of memristive circuits that realize the computing behavior of Learning Cellular Automata. An example of this methodology is provided with the description of the implementation of edge detection for image processing.