Wave Algorithm: A Powerful Tool for Procedural Generation
The wave function collapse (WFC) algorithm is a powerful tool for procedural generation, which is the process of creating content algorithmically. WFC is often used to generate game levels, mazes, and other types of procedurally generated content.
The WFC algorithm works by propagating a wave of possibilities through a grid of cells. Each cell in the grid can contain a number of different possible values. For example, a cell in a maze game could contain the values "wall," "path," or "door."
The WFC algorithm starts by collapsing the wave function of a single cell to one of its possible values. This is usually done by randomly selecting one of the possible values. Once the wave function of a cell has been collapsed, the algorithm propagates the new wave to the neighboring cells.
The propagation process works by eliminating any possible values from the neighboring cells that are not compatible with the collapsed value in the center cell. For example, if the center cell in a maze game has been collapsed to the value "wall," then the algorithm would eliminate the value "path" from all of the neighboring cells.
The WFC algorithm repeats the collapsing and propagation process until all of the cells in the grid have had their wave functions collapsed. Once this happens, the algorithm has generated a complete and consistent procedurally generated world.
Example: Generating a Maze
Here is a simple example of how the WFC algorithm can be used to generate a maze:
Start with a grid of empty cells.
Randomly collapse the wave function of a single cell to the value "wall."
Propagate the new wave to the neighboring cells, eliminating any possible values that are not compatible with the collapsed value in the center cell.
Repeat steps 2 and 3 until all of the cells in the grid have had their wave functions collapsed.
Once the algorithm has finished, the grid will contain a complete and consistent maze, with walls and paths.
Advantages of the Wave Function Collapse Algorithm
The WFC algorithm has a number of advantages over other procedural generation algorithms. First, it is very efficient, meaning that it can generate large and complex worlds quickly. Second, it is very flexible, meaning that it can be used to generate a wide variety of different types of procedurally generated content.
Disadvantages of the Wave Function Collapse Algorithm
The main disadvantage of the WFC algorithm is that it can be difficult to tune correctly. The algorithm has a number of parameters that can be adjusted, and it is important to find the right settings for the type of content that you are trying to generate.
Applications of the Wave Function Collapse Algorithm
The WFC algorithm has been used to generate a wide variety of different types of procedurally generated content, including:
Game levels
Mazes
Dungeons
Forests
Cities
Music
Art
The WFC algorithm is a powerful tool for procedural generation, and it is likely to be used in even more applications in the future.
Conclusion
The wave function collapse (WFC) algorithm is a powerful tool for procedural generation. It is efficient, flexible, and can be used to generate a wide variety of different types of content. However, the WFC algorithm can be difficult to tune correctly.
If you are interested in learning more about the WFC algorithm, there are a number of resources available online. There are also a number of open source implementations of the WFC algorithm that you can use to get started.