In this paper, the hexagonal approach was proposed for modeling the functioning of cerebral cortex, especially, the processes of learning and recognition of visual information. This approach is based on the real neurophysiological data of the structure and functions of cerebral cortex. Distinctive characteristic of the proposed neural network is the hexagonal arrangement of excitatory connections between neurons that enable the spreading or cloning of information on the surface of neuronal layer. Cloning of information and modification of the weight of connections between neurons are used as the basic principles for learning and recognition processes. Computer simulation of the hexagonal neural network indicated a suitability and prospectiveness of proposed approach in the creation, together with other modern concepts, of artificial neural network which will realize the most complicated processes that take place in the brain of living beings, such as short-term and long-term memory, ep...