3D A Pathfinding on Spanning Trees

[FunKite]

This still image of my interactive viewer demonstrates A* pathfinding on a spanning tree generated with Randomized Prim's Algorithm on a Body-Centered Cubic (BCC) lattice with 14-neighbor connectivity. Crucially, because the underlying structure is a tree (not a general graph), there is exactly one valid path between any two nodes—A*'s challenge isn't finding the optimal route among many options, but rather discovering that single path through the tree's structure while exploring dead-end branches. Green octahedra mark the unique solution path from start to goal, while red octahedra show all 52,284 dead-end nodes that A* explored during its search—even though the final path contains only 212 nodes. This visualization reveals how A* navigates constrained spaces: with seed 41, the algorithm explores 247x more nodes than necessary before finding the only valid route, demonstrating both the algorithm's systematic exploration strategy and the challenge of searching without global knowledge of the tree topology. The interactive viewer is not in Rust so I probably won't pollute my Rust repo with it.