## Random Runner Classic

Maze generation algorithms are automated methods for the creation of mazes.

This maze generated by modified version of Prim's algorithm, below.

## Graph theory based methods

Animation of graph theory based method (randomized depth-first search)
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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 Gshown in blue, and its dual Fshown in yellow. Second, computer traverses F using a chosenalgorithm, such as a depth-first search, coloring the path red.During the traversal, whenever a red edge crosses over a blue edge,the blue edge is removed.Finally, when all vertices of F have been visited, F is erasedand two edges from G, one for the entrance and one for the exit, are removed.

### Randomized depth-first search

Animation of generator using depth-first search

This algorithm, also known as the 'recursive backtracker' algorithm, is a randomized version of the depth-first search algorithm.

Frequently implemented with a stack, this approach is one of the simplest ways to generate a maze using a computer. Consider the space for a maze being a large grid of cells (like a large chess board), each cell starting with four walls. Starting from a random cell, the computer then selects a random neighbouring cell that has not yet been visited. The computer removes the wall between the two cells and marks the new cell as visited, and adds it to the stack to facilitate backtracking. The computer continues this process, with a cell that has no unvisited neighbours being considered a dead-end. When at a dead-end it backtracks through the path until it reaches a cell with an unvisited neighbour, continuing the path generation by visiting this new, unvisited cell (creating a new junction). This process continues until every cell has been visited, causing the computer to backtrack all the way back to the beginning cell. We can be sure every cell is visited.

As given above this algorithm involves deep recursion which may cause stack overflow issues on some computer architectures. The algorithm can be rearranged into a loop by storing backtracking information in the maze itself. This also provides a quick way to display a solution, by starting at any given point and backtracking to the beginning.

Horizontal Passage Bias

Mazes generated with a depth-first search have a low branching factor and contain many long corridors, because the algorithm explores as far as possible along each branch before backtracking.

#### Recursive implementation

Randomized depth-first search on a hexagonal grid

The depth-first search algorithm of maze generation is frequently implemented using backtracking. This can be described with a following recursive routine:

1. Given a current cell as a parameter,
2. Mark the current cell as visited
3. While the current cell has any unvisited neighbour cells
1. Choose one of the unvisited neighbours
2. Remove the wall between the current cell and the chosen cell
3. Invoke the routine recursively for a chosen cell

which is invoked once for any initial cell in the area.

#### Iterative implementation

A disadvantage of the first approach is a large depth of recursion – in the worst case, the routine may need to recur on every cell of the area being processed, which may exceed the maximum recursion stack depth in many environments. As a solution, the same backtracking method can be implemented with an explicit stack, which is usually allowed to grow much bigger with no harm.

1. Choose the initial cell, mark it as visited and push it to the stack
2. While the stack is not empty
1. Pop a cell from the stack and make it a current cell
2. If the current cell has any neighbours which have not been visited
1. Push the current cell to the stack
2. Choose one of the unvisited neighbours
3. Remove the wall between the current cell and the chosen cell
4. Mark the chosen cell as visited and push it to the stack

### Randomized Kruskal's algorithm

An animation of generating a 30 by 20 maze using Kruskal's algorithm.

This algorithm is a randomized version of Kruskal's algorithm.

1. Create a list of all walls, and create a set for each cell, each containing just that one cell.
2. For each wall, in some random order:
1. If the cells divided by this wall belong to distinct sets:
1. Remove the current wall.
2. Join the sets of the formerly divided cells.

There are several data structures that can be used to model the sets of cells. An efficient implementation using a disjoint-set data structure can perform each union and find operation on two sets in nearly constant amortized time (specifically, ${displaystyle O(alpha (V))}$ time; ${displaystyle alpha (x)<5}$ for any plausible value of ${displaystyle x}$), so the running time of this algorithm is essentially proportional to the number of walls available to the maze.

It matters little whether the list of walls is initially randomized or if a wall is randomly chosen from a nonrandom list, either way is just as easy to code.

Because the effect of this algorithm is to produce a minimal spanning tree from a graph with equally weighted edges, it tends to produce regular patterns which are fairly easy to solve.

### Randomized Prim's algorithm

An animation of generating a 30 by 20 maze using Prim's algorithm.

This algorithm is a randomized version of Prim's algorithm.

2. Pick a cell, mark it as part of the maze. Add the walls of the cell to the wall list.
3. While there are walls in the list:
1. Pick a random wall from the list. If only one of the two cells that the wall divides is visited, then:
1. Make the wall a passage and mark the unvisited cell as part of the maze.
2. Add the neighboring walls of the cell to the wall list.
2. Remove the wall from the list.

Note that simply running classical Prim's on a graph with random edge weights would create mazes stylistically identical to Kruskal's, because they are both minimal spanning tree algorithms. Instead, this algorithm introduces stylistic variation because the edges closer to the starting point have a lower effective weight.

#### Modified version

Although the classical Prim's algorithm keeps a list of edges, for maze generation we could instead maintain a list of adjacent cells. If the randomly chosen cell has multiple edges that connect it to the existing maze, select one of these edges at random. This will tend to branch slightly more than the edge-based version above.

#### Simplified version

The algorithm can be simplfied even further by randomly selecting cells that neighbour already-visited cells, rather than keeping track of the weights of all cells or edges.

It will usually be relatively easy to find the way to the starting cell, but hard to find the way anywhere else.

### Wilson's algorithm

All the above algorithms have biases of various sorts: depth-first search is biased toward long corridors, while Kruskal's/Prim's algorithms are biased toward many short dead ends. Wilson's algorithm,[1] on the other hand, generates an unbiased sample from the uniform distribution over all mazes, using loop-erased random walks.

We begin the algorithm by initializing the maze with one cell chosen arbitrarily. Then we start at a new cell chosen arbitrarily, and perform a random walk until we reach a cell already in the maze—however, if at any point the random walk reaches its own path, forming a loop, we erase the loop from the path before proceeding. When the path reaches the maze, we add it to the maze. Then we perform another loop-erased random walk from another arbitrary starting cell, repeating until all cells have been filled.

This procedure remains unbiased no matter which method we use to arbitrarily choose starting cells. So we could always choose the first unfilled cell in (say) left-to-right, top-to-bottom order for simplicity.

### Aldous-Broder algorithm

The Aldous-Broder algorithm also produces uniform spanning trees.

1. Pick a random cell as the current cell and mark it as visited.
2. While there are unvisited cells:
1. Pick a random neighbour.
2. If the chosen neighbour has not been visited:
1. Remove the wall between the current cell and the chosen neighbour.
2. Mark the chosen neighbour as visited.
3. Make the chosen neighbour the current cell.

## Recursive division method

Illustration of Recursive Division
original chamberdivision by two wallsholes in wallscontinue subdividing..completed
step 1
step 2
step 3
step 4
step 5

Mazes can be created with recursive division, an algorithm which works as follows: Begin with the maze's space with no walls. Call this a chamber. Divide the chamber with a randomly positioned wall (or multiple walls) where each wall contains a randomly positioned passage opening within it. Then recursively repeat the process on the subchambers until all chambers are minimum sized. This method results in mazes with long straight walls crossing their space, making it easier to see which areas to avoid.

## Random Runner Classic Wow

Recursive Maze generation

For example, in a rectangular maze, build at random points two walls that are perpendicular to each other. These two walls divide the large chamber into four smaller chambers separated by four walls. Choose three of the four walls at random, and open a one cell-wide hole at a random point in each of the three. Continue in this manner recursively, until every chamber has a width of one cell in either of the two directions.

## Simple algorithms

3D version of Prim's algorithm. Vertical layers are labeled 1 through 4 from bottom to top. Stairs up are indicated with '/'; stairs down with ', and stairs up-and-down with 'x'. Source code is included with the image description.

Other algorithms exist that require only enough memory to store one line of a 2D maze or one plane of a 3D maze. Eller's algorithm prevents loops by storing which cells in the current line are connected through cells in the previous lines, and never removes walls between any two cells already connected.[2] The Sidewinder algorithm starts with an open passage along the entire the top row, and subsequent rows consist of shorter horizontal passages with one connection to the passage above. The Sidewinder algorithm is trivial to solve from the bottom up because it has no upward dead ends.[3] Given a starting width, both algorithms create perfect mazes of unlimited height.

Most maze generation algorithms require maintaining relationships between cells within it, to ensure the end result will be solvable. Valid simply connected mazes can however be generated by focusing on each cell independently. A binary tree maze is a standard orthogonal maze where each cell always has a passage leading up or leading left, but never both. To create a binary tree maze, for each cell flip a coin to decide whether to add a passage leading up or left. Always pick the same direction for cells on the boundary, and the end result will be a valid simply connected maze that looks like a binary tree, with the upper left corner its root. As with Sidewinder, the binary tree maze has no dead ends in the directions of bias.

A related form of flipping a coin for each cell is to create an image using a random mix of forward slash and backslash characters. This doesn't generate a valid simply connected maze, but rather a selection of closed loops and unicursal passages. (The manual for the Commodore 64 presents a BASIC program using this algorithm, but using PETSCII diagonal line graphic characters instead for a smoother graphic appearance.)

## Cellular automaton algorithms

Certain types of cellular automata can be used to generate mazes.[4] Two well-known such cellular automata, Maze and Mazectric, have rulestrings B3/S12345 and B3/S1234.[4] In the former, this means that cells survive from one generation to the next if they have at least one and at most five neighbours. In the latter, this means that cells survive if they have one to four neighbours. If a cell has exactly three neighbours, it is born. It is similar to Conway's Game of Life in that patterns that do not have a living cell adjacent to 1, 4, or 5 other living cells in any generation will behave identically to it.[4] However, for large patterns, it behaves very differently from Life.[4]

For a random starting pattern, these maze-generating cellular automata will evolve into complex mazes with well-defined walls outlining corridors. Mazecetric, which has the rule B3/S1234 has a tendency to generate longer and straighter corridors compared with Maze, with the rule B3/S12345.[4] Since these cellular automaton rules are deterministic, each maze generated is uniquely determined by its random starting pattern. This is a significant drawback since the mazes tend to be relatively predictable.

Like some of the graph-theory based methods described above, these cellular automata typically generate mazes from a single starting pattern; hence it will usually be relatively easy to find the way to the starting cell, but harder to find the way anywhere else.

## References

1. ^Wilson, David Bruce (May 22–24, 1996). 'Generating random spanning trees more quickly than the cover time'. Proceedings of the Twenty-eighth Annual ACM Symposium on Theory of Computing. Symposium on Theory of Computing. Philadelphia: ACM. pp. 296–303. CiteSeerX10.1.1.47.8598. doi:10.1145/237814.237880. ISBN0-89791-785-5.
2. ^Jamis Buck (29 December 2010). 'Maze Generation: Eller's Algorithm'.
3. ^Jamis Buck (3 February 2011). 'Maze Generation: Sidewinder Algorithm'.
4. ^ abcdeNathaniel Johnston; et al. (21 August 2010). 'Maze - LifeWiki'. LifeWiki. Retrieved 1 March 2011.

• Think Labyrinth: Maze algorithms (details on these and other maze generation algorithms)
• Implementations of DFS maze creation algorithm in multiple languages at Rosetta Code
Designer(s) Richard Garfield Wizards of the Coast 2 15 minutes ~ 45 minutes Some 9+ Card playingArithmetic

Netrunner is an out-of-print collectible card game (CCG) designed by Richard Garfield, the creator of Magic: The Gathering. It was published by Wizards of the Coast and introduced in April 1996.[1] The game took place in the setting for the Cyberpunk 2020role-playing game (RPG), but it also drew from the broader cyberpunk genre.

In 2012, Fantasy Flight Games released Android: Netrunner, a new card game based on Netrunner, under license from Wizards of the Coast. The new game uses Fantasy Flight Games' Living Card Game release format (as used in their Warhammer: Invasion, A Game of Thrones, Call of Cthulhu, and Lord of the Rings games), and shares the cyberpunk setting of their Android board game.

## Gameplay

Netrunner depicts cyberspace combat between a global mega-corporation (the Corp) and a hacker (the Runner). The Corp aims to complete its secret agendas before the Runner can hack in and steal data. It isn't easy, though, as the Corp has strong defensive data forts protected by malevolent computer programs known as ICE (short for Intrusion Countermeasures Electronics). Runners must use special programs of their own, called icebreakers, to break through and steal the hidden plans. All this is paid for in the game by bits (representing currency), which are earned and spent during the course of play.[2]

An interesting feature of Netrunner is its asymmetry: each side has different abilities and uses completely different cards distinguished by alternate card backs. This contrasts with most other CCGs, which usually depict a 'battle between peers' where each opponent draws upon the same card pool. While a player does not have to play both sides except in tournament play, many players believe that a firm understanding of both leads to better overall player ability.

The Cyberpunk 2020 supplement Rache Bartmoss' Brainware Blowout featured rules on using Netrunner cards instead of the RPG's existing system to simulate netrunning during game sessions. It also gave conversions to the RPG of some of the cards in the base set (the rest having been mentioned in one book or another).

## Expansion sets

• Netrunner base set (aka Limited, v1.0) - 374 cards - Release Date: April 26, 1996
• Proteus (v2.1) - 154 cards - Release Date: September 1996[3]
• Silent Impact - Never released, development halted by WotC. However, a series of six cards labelled 'v2.0' were issued as promotional cards for a planned, but never released, Netrunner 2.0 core set. Even though originally appearing in Netrunner 1.0, these six cards have been revised for 2.0 and feature new artwork as well as revised game text. The six cards in question are Forged Activation Orders, misc.for-sale, The Shell Traders, Pacifica Regional AI, Bizarre Encryption Scheme, and New Galveston City Grid. These cards are extremely rare.
• Classic (v2.2) - 52 cards from the Silent Impact set. Release Date: November 1999

Several fan-made expansions have been created for Netrunner, and released online. Many of them have been sanctioned for tournament play.[4]

## Webrunner

Netrunner launched with a proto-alternate reality game called Webrunner: The Hidden Agenda, which cast players as hackers against the evil Futukora corporation. Players broke through seven puzzle-themed 'gates' to get the secret data ('agenda'). The popular game was the first online game tied into a product release, making the front page of the New York Times technology section.[5]

A sequel, Webrunner II: The Forbidden Code, followed on release of the Proteus expansion. In this, players were cast as security chiefs beset by hackers.

## Online gameplay

Netrunner was playable online through CCG Workshop in the past, but it was shut down by Wizards of the Coast. It is now possible to play Netrunner online using Magic Workstation on Runners' Net, a site which also holds IRC chats and forums to discuss the game. Players may also use other CCG engines such as LackeyCCG or Gccg, which allows players to build and share plugins for different card games and play the games online.This game can now be played on the OCTGN online game system.

## Product ownership

Zvi Mowshowitz, a well-known Magic: The GatheringPro Tour player, attempted to purchase the license for Netrunner from Wizards of the Coast after the company stopped producing the game. Negotiations, however, fell apart without any revival of the game or transfer of ownership.

In 2012, Fantasy Flight Games announced that they were releasing a modified version of Netrunner, under license from Wizards of the Coast, called Android: Netrunner.

In 2018, Fantasy Flight Games announced that their partnership with Wizards of the Coast to license development of the game was concluding. Starting October 22, 2018, Fantasy Flight will no longer sell Netrunner products.[6]

## Reception

Andy Butcher reviewed Netrunner for Arcane magazine, rating it a 9 out of 10 overall.[7] Butcher comments that 'Netrunner is almost without fault. It's certainly the best new card game in the last year, and arguably the best since Magic started it all. Richard Garfield has done it again.'[7]

Netrunner was lauded by critics, such as InQuest magazine, for its balanced game play and impressive artwork.[8] In 1999 Pyramid magazine named Netrunner as one of 'The Millennium's Most Underrated Games'. According to editor Scott Haring, 'among the connoisseurs of the card game design art, Netrunner is considered to be one of the best-designed games ever.'[9]

## References

1. ^Miller, John Jackson (2003), Scrye Collectible Card Game Checklist & Price Guide, Second Edition, pp. 411–414.
2. ^Lin, Jim (May 1996), 'Up and Running', The Duelist (#10), pp. 86–88
3. ^Haines, Kathryn L. (September 1996), 'A Look at Proteus', The Duelist (#12), pp. 59–66
4. ^'Netrunner Online Hub: Card Sets'. Netrunner Online. Retrieved 2012-09-17.
5. ^Rothstein, Edward (February 19, 1996). 'Netrunner: Hacking With a Shuffled Deck'. The New York Times. Retrieved August 17, 2013.
6. ^'Jacking Out'. www.fantasyflightgames.com. Retrieved 2018-06-08.
7. ^ abButcher, Andy (May 1996). 'Games Reviews'. Arcane. Future Publishing (6): 56–59.
8. ^http://www.oocities.org/theshortcircuit/basics/inquest.html
9. ^Haring, Scott D. (1999-11-25). 'Second Sight: The Millennium's Most Influential Company and The Millennium's Most Underrated Game'. Pyramid (online). Retrieved 2008-02-16.