The paper addresses a novel evolving functional fuzzy modeling algorithm using hyperboxes and min-max fuzzy granulation. Data space granulation is done as data are input, and undergoes never ending adaptation using expansion and reduction operations to encompass new information. A fuzzy rule is assigned to each hyperbox using Gaussian membership functions in the rule antecedents, and affine functions in the rule consequents. The algorithm is fast, simple, and interpretable. Computational evaluation using time series modeling and nonlinear system identification experiments shows that the granular evolving min-max fuzzy modeling algorithm outperforms current state of the art evolving algorithms counterparts.