Immersive Algorithms: Better Visualization with Less Information

Visualizing algorithms, such as drawings, slideshow presentations, animations, videos, and software tools, is a key concept to enhance and support student learning. A typical visualization of an algorithm show the data and then perform computation on the data. For instance, a standard visualization of a standard binary search on an array shows an array of sorted numbers and then illustrate the action of the algorithm in a step-by-step fashion. However, this approach does not fully capture the computational environment from the perspective of the algorithm. Specifically, the algorithm does not "see" the full sorted array, but only the single position that it accesses during each step of the computation. To fix this discrepancy we introduce the \emph{immersive principle} that states that at any point in time, the displayed information should closely match the information accessed by the algorithm. We give several examples of immersive visualizations of basic algorithms and data structures, discuss methods for implementing it, and briefly evaluate it.