Suppose you are asked to choose randomly between left or right 100 times, would you expect the average of your choices to be roughly even or to have a bias? In the literature, human randomness falls on a spectrum from being close to unbiased to very biased in random choices. To create a model with a neural implementation of human randomness, unsupervised artificial neural networks were used to generate a random representation of binary numbers. These random representations were tested with both orthogonal and correlated stimuli as inputs and the properties of all outputs are discussed. An example of how to bias this generated randomness to model different cognitive processes is shown under two conditions, where random decisions are biased for desired outcomes and for list exhaustion (random sampling without replacement). Other possible uses for this method of generating randomness in cognitive modelling are discussed.