A specific characteristic of the modeling offered in the present paper is the hexagonal structure of neural network organization. Four basic principles of the visual cortex modeling were discussed as follows: the equal-distant-connections between neurons, the information cloning and spreading on the surface of cortex as an invariant analysis of visual objects, the competition mechanism, and the orientation preferences of neurons. Distinctive characteristic of the proposed neural network topology 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 topology indicated a suitability and perspective of the proposed approach. The described neural network model was approbated by the computer program written on Delfi 3 language named the first order hexagon brainware (HBW-1).