hexmazen

Hexmazen is a term used in discussions of hexagonal maze systems to refer to a labyrinth laid out on a hexagonal grid. The construction exploits six-neighbor connectivity and hex-edge walls, producing path structures and symmetry that differ from those on square grids. The name combines hex, for hexagonal tiling, with maze, indicating a navigational puzzle rather than a fixed object.

In formal terms, a hexmazen can be modeled as a planar graph whose vertices are hexagonal cells and whose edges connect neighboring cells that are not separated by walls. A designated start cell and a goal cell define the path to be found. The difficulty emerges from wall placement, wall density, and additional elements such as keys and doors.

Generation and algorithms: Hexmazen are commonly produced using adaptations of standard maze-generation algorithms to hex grids, such as recursive backtracking, randomized Prim’s, or depth-first search, with walls removed between adjacent unvisited cells. Pathfinding on hexmazes uses A*, Dijkstra’s, or breadth-first search, with hex-distance as the metric.

Variants and design considerations: Hexmazes can vary in density, connectivity, and symmetry. They may include multiple entrances or exits, looping corridors, or 3D extensions on stacked hex grids. The hex tiling’s sixfold symmetry influences pattern formation and perceived difficulty.

Use and reception: Hexmazen appear in puzzle collections, educational materials for graph theory and algorithms, and digital games that explore hex-grid navigation. They serve as accessible examples of hex tiling, maze generation, and pathfinding for learners and designers.