This modeling study investigates whether an orderly convergence of neuronal selectivities from cortical areas V1 and V2 can produce the fine structure of shape selective receptive fields found in area V4 recordings. A model of fast object recognition in the ventral visual pathway is made of spiking neurons having simple convergent functional micro-architectures. The model is based on recent findings about the convergent properties of V2 neurons on V1 afferents and makes a novel proposal for how V4 neurons may create selectivity for local curvature through the orderly convergence of different types of afferent inputs from V2. The model also demonstrates a novel method for simulating spiking neurons using tensor programming and GPU hardware: Assuming that convergent functional micro-architectural patterns repeat in topographically organized visual space, the details of individual unit depolarization and spike time is modeled using convolution operations augmented with a custom tensor model of post-synaptic potentials. The model, described as Organic Convolution, suggests that convergent selectivity patterns equivalent to convolution can be created by developmental mechanisms, laying the foundation for object recognition before an organism learns from experience. This study does not investigate developmental mechanisms directly but, using convergent patterns that are hand crafted to match neurophysiological data, shows that the mechanisms giving rise to object recognition may be very simple. As a result, the model suggests an alternative point of view on how deep neural networks may relate to biology.