Construction of a smooth multivariate simulation environment from a finite one-to-one mapping

Complex computer-simulated environments are often sought in which autonomous agents can interact and their capabilities can be examined. Creating such simulated environments, however, can often be regarded as a very non-trivial undertaking. This work demonstrates how one can construct a smooth and continuous online environment which is easily computable and runs in polynomial time using a finite number of example function input/output pairs. Due to the manner of its construction, the newly created smooth mapping will give the same or similar outputs as the original one-to-one function it was derived from. Also, having no discontinuities, the constructed smooth mapping will not break should it be made to accept out-of-range or erroneous actions from an agent which engages it. Ultimately, this algorithm is used to construct an integral portion of a sequential environment which is utilized in a study to simulate the acquisition of phoneme sequence generating ability thought to occur in the brain.