A computer system generates transition effects for use on a visual display. The system includes a binary table for describing a transition effect and a method for ordering the rows in the table to produce the transition. The table includes an arbitrary number of rows, each row representing a cell (group of picture elements) on the display. A numerical value, based on any function of cell location, is associated with each cell. The table is then sorted according to the numerical values. Each row in the sorted table drives a step in the transition effect. The cells described by the various rows are changed in sorted order to display the material from the image being transitioned-to. The sequence of processing of the rows causes the desired transition effect. By varying the function used to order the rows, an infinite variety of transition effects can be created.