A method and apparatus for constructing one of a neuroscience-inspired artificial neural network and a neural network array comprises one of a neuroscience-inspired dynamic architecture, a dynamic artificial neural network array and a neural network array of electrodes associated with neural tissue such as a brain, the method and apparatus having a special purpose display processor. The special purpose display processor outputs a display over a period of selected reference time units to demonstrate a neural pathway from, for example, one or a plurality of input neurons through intermediate destination neurons to an output neuron in three-dimensional space. The displayed neural network may comprise neurons and synapses in different colors and may be utilized, for example, to show the behavior of a neural network for classifying hand-written digits between values of 0 and 9 or recognizing vertical/horizontal lines in a grid image of lines.