A computer-implemented for reducing memory requirements for a user interface method includes generating, by one or more processors, a first matrix of symbols with columns that correspond to reels of cyclical symbols. The reels are configured to be rendered in adjacent sections of a display. The method further includes rotating, by one or more processors, each reel by a random amount responsive to receiving a spinning instruction. The method includes configuring a first reel to occupy both a first section of the display associated with the first reel and a second section of the display associated with an adjacent reel so that the adjacent reel will not be rendered when a pattern of symbols of the rendered reels is determined to correspond to a particular pattern. Data that represents the symbols of the reels is maintained in a shadow matrix stored in memory. The one or more processors determine the existence of particular patterns from the shadow matrix and search a table in memory for scores associated with the patterns. Data in the shadow matrix is copied between cells of the shadow matrix to correspond to the rendered reels in such a way as to obviate increasing the size of the table. This, in turn, reduces memory requirements associated with the rendering of the reels.