GoKawiilMazes in general (and hence algorithms to create Mazes) can be organized along seven different classifications. These are: Dimension, Hyperdimension, Topology, Tessellation, Routing, Texture, and Focus. A Maze can take one item from each of the classes in any combination.
Dimension: The dimension class is basically how many dimensions in space the Maze covers. Types are:
2D : Most Mazes, either on paper or life size, are this dimension, in which it's always possible to display the plan on the sheet of paper and navigate it without overlapping any other passages in the Maze.
Most Mazes, either on paper or life size, are this dimension, in which it's always possible to display the plan on the sheet of paper and navigate it without overlapping any other passages in the Maze. 3D : A three dimensional Maze is one with multiple levels, where (in the orthogonal case at least) passages may go up and down in addition to the four compass directions. A 3D Maze is often displayed as an array of 2D levels, with "up" and "down" staircase indicators.
A three dimensional Maze is one with multiple levels, where (in the orthogonal case at least) passages may go up and down in addition to the four compass directions. A 3D Maze is often displayed as an array of 2D levels, with "up" and "down" staircase indicators. Higher dimensions : It's possible to have 4D and higher dimension Mazes. These are sometimes rendered as 3D Mazes, with special "portals" to travel through the 4th dimension, e.g. "past" and "future" portals.
It's possible to have 4D and higher dimension Mazes. These are sometimes rendered as 3D Mazes, with special "portals" to travel through the 4th dimension, e.g. "past" and "future" portals. Weave: A weave Maze is basically a 2D (or more accurately a 2.5D) Maze, but where passages can overlap each other. In display it's generally obvious what's a dead end and what's a passage that goes underneath another. Life size Mazes that have bridges connecting one portion of the Maze to another are partially Weave.
Hyperdimension: The hyperdimension class refers to the dimension of the object you move through the Maze, as opposed to the dimension of the Maze environment itself. Types are:
Non-hypermaze : Virtually all Mazes, even those in higher dimensions or with special rules, are normal non-hypermazes. In them you work with a point or small object, such as a marble or yourself, which you move from point to point, and the path behind you forms a line. There's an easily countable number of choices at each point.
Virtually all Mazes, even those in higher dimensions or with special rules, are normal non-hypermazes. In them you work with a point or small object, such as a marble or yourself, which you move from point to point, and the path behind you forms a line. There's an easily countable number of choices at each point. Hypermaze: A hypermaze is where the solving object is more than just a point. A standard hypermaze (or a hypermaze of the 1st order) consists of a line where as you bend and move it the path behind it forms a surface. A hypermaze can only exist in a 3D or higher dimension environment, where the entrance to a hypermaze is also a line instead of a point. A hypermaze is fundamentally different since you need to be aware of and work with multiple parts along the line at the same time, where there's nearly an infinite number of states and things you can do with the line at any time. The solving line is infinite, or the endpoints are fixed outside of the hypermaze, to prevent one from crumpling the line into a point, which could then be treated as a non-hypermaze.
A hypermaze is where the solving object is more than just a point. A standard hypermaze (or a hypermaze of the 1st order) consists of a line where as you bend and move it the path behind it forms a surface. A hypermaze can only exist in a 3D or higher dimension environment, where the entrance to a hypermaze is also a line instead of a point. A hypermaze is fundamentally different since you need to be aware of and work with multiple parts along the line at the same time, where there's nearly an infinite number of states and things you can do with the line at any time. The solving line is infinite, or the endpoints are fixed outside of the hypermaze, to prevent one from crumpling the line into a point, which could then be treated as a non-hypermaze. Hyperhypermaze: Hypermazes can be of arbitrarily high dimension. A hyperhypermaze (or a hypermaze of the 2nd order) increases the dimension of the solving object again. Here the solving object is a plane, where as you move it the path behind you forms a solid. A hyperhypermaze can only exist in a 4D or higher dimension environment.
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