This study is focused on the development of the cortex-like visual object recognition system. We propose a general framework, which consists of three hierarchical levels (modules). These modules functionally correspond to the V1, V4 and IT areas. Both bottom-up and top-down connections between the hierarchical levels V4 and IT are employed. The higher the degree of matching between the input and the preferred stimulus, the shorter the response time of the neuron. Therefore information about a single stimulus is distributed in time and is transmitted by the waves of spikes. The reciprocal connections and waves of spikes implement predictive coding: an initial hypothesis is generated on the basis of information delivered by the first wave of spikes and is tested with the information carried by the consecutive waves. The development is considered as extraction and accumulation of features in V4 and objects in IT. Once stored a feature can be disposed, if rarely activated. This cause update of feature repository. Consequently, objects in IT are also updated. This illustrates the growing process and dynamical change of topological structures of V4, IT and connections between these areas.