Dimensional Fusion: The Cartesian Product of Cubes

This simulator makes the abstract idea of "fusing dimensions" concrete and exact: pick two low-dimensional cubes — a point, a line segment or a square — and watch them fuse into a single higher-dimensional cube through the graph Cartesian product, the same construction that turns a square and a line into an ordinary 3D cube, or two squares into a 4D tesseract. A fusion-progress slider animates separate copies of one factor sweeping together into the true product coordinates while live counters track the resulting dimension, vertex count and edge count from the exact combinatorial formulas, and a 4D rotation control lets you spin the tesseract case through its extra axis and watch its 3D projection breathe.