Maze generation algorithm
automated method for the creation of mazes
Maze generation algorithms are automated methods for the creation of mazes.
Graph theory based methods
A maze can be generated by starting with a predetermined arrangement of cells (most commonly a rectangular grid but other arrangements are possible) with wall sites between them. This predetermined arrangement can be considered as a connected graph with the edges representing possible wall sites and the nodes representing cells. The purpose of the maze generation algorithm can then be considered to be making a subgraph in which it is challenging to find a route between two particular nodes.
If the subgraph is not connected, then there are regions of the graph that are wasted because they do not contribute to the search space. If the graph contains loops, then there may be multiple paths between the chosen nodes. Because of this, maze generation is often approached as generating a random spanning tree. Loops, which can confound naive maze solvers, may be introduced by adding random edges to the result during the course of the algorithm.
The animation shows the maze generation steps for a
graph that is not on a rectangular grid.
First, the computer creates a random planar graph G
shown in blue, and its dual F
shown in yellow.
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