![References:
Ascani, E (2011, October 4). Epic Game of Life. Retrieved April 4, 2016, from
https://www.youtube.com/watch?v=C2vgICfQawE
Codd, E. F. (1968). Cellular automata [Http://dl.acm.org/citation.cfm?id=1098682]. New York:
Academic Press. Retrieved April 4, 2016.
DeAngelis, M. (2016, February 29). Cat Maze Disguised as Bookshelves. Retrieved April 4, 2016, from
http://www.cluttermagazine.com/news/2016/02/cat-maze-disguised-bookshelves
Gardner, M. (1983). Wheels, life, and other mathematical amusements (Chp 20-22). New York: W.H.
Freeman.
Levy, S. (1993). Artificial life: A report from the frontier where computers meet biology. New York:
Vintage Books.
Pajot, T. (n.d.). Printed Circuit Board. Retrieved April 4, 2016, from
http://www.123rf.com/photo_10607345_printed-circuit-board.html](https://image.slidesharecdn.com/47e929d7-3f6b-414c-a6ca-15106824f4e3-160406042647/85/Cellular-Automata-for-Pathfinding-120-320.jpg)
Cellular Automata for Pathfinding
- 1. A Fault tolerant, Parallelizable incremental approach for real time environments Steve Wilson
- 2. Overview: What is a cellular automata How it is related to other automata What is path finding Other approaches to pathfinding Why a new method ? The cellular approach Pros and Cons of using cellular automata
- 4. Whatisacellularautomata: Types of “automata” or “machines”
- 5. Whatisacellularautomata: Types of automata Finite state machine
- 6. Whatisacellularautomata: Types of automata Finite state machine One or more states
- 7. Whatisacellularautomata: Types of automata Finite state machine One or more states Transition rules
- 8. Whatisacellularautomata: Types of automata Finite state machine One or more states Transition rules Input
- 9. Whatisacellularautomata: Types of automata Finite state machine Push down automata
- 10. Whatisacellularautomata: Types of automata Finite state machine Push down automata One or more states
- 11. Whatisacellularautomata: Types of automata Finite state machine Push down automata One or more states Transition rules
- 12. Whatisacellularautomata: Types of automata Finite state machine Push down automata One or more states Transition rules Input
- 13. Whatisacellularautomata: Types of automata Finite state machine Push down automata One or more states Transition rules Input Stack
- 14. Whatisacellularautomata: Types of automata Finite state machine Push down automata Turing machine
- 15. Whatisacellularautomata: Types of automata Finite state machine Push down automata Turing machine One or more states
- 16. Whatisacellularautomata: Types of automata Finite state machine Push down automata Turing machine One or more states Transition rules
- 17. Whatisacellularautomata: Types of automata Finite state machine Push down automata Turing machine One or more states Transition rules Tape
- 18. Whatisacellularautomata: Types of automata Finite state machine Push down automata Turing machine Cellular Automata
- 19. Whatisacellularautomata: Types of automata Finite state machine Push down automata Turing machine Cellular Automata Two or more states
- 20. Whatisacellularautomata: Types of automata Finite state machine Push down automata Turing machine Cellular Automata Two or more states Transition rules
- 21. Whatisacellularautomata: Types of automata Finite state machine Push down automata Turing machine Cellular Automata Two or more states Transition rules Neighbor states
- 23. Whatisacellularautomata: Basically a Cellular automata is a collection of connected finite state machines
- 24. Whatisacellularautomata: Basically a Cellular automata is a collection of connected finite state machines Subtypes of cellular automata
- 25. Whatisacellularautomata: Basically a Cellular automata is a collection of connected finite state machines Subtypes of cellular automata Graph
- 26. Whatisacellularautomata: Basically a Cellular automata is a collection of connected finite state machines Subtypes of cellular automata Graph Cells are connected by “edges”
- 27. Whatisacellularautomata: Basically a Cellular automata is a collection of connected finite state machines Subtypes of cellular automata Graph Grid
- 28. Whatisacellularautomata: Basically a Cellular automata is a collection of connected finite state machines Subtypes of cellular automata Graph Grid Cells are arranged uniformly in a pattern and connected spatially
- 29. Whatisacellularautomata: Basically a Cellular automata is a collection of connected finite state machines Subtypes of cellular automata Graph Grid Subdivision
- 30. Whatisacellularautomata: Basically a Cellular automata is a collection of connected finite state machines Subtypes of cellular automata Graph Grid Subdivision Used extensively in modeling, cells are connected spatially in a non-uniform manner
- 31. Whatisacellularautomata: Basically a Cellular automata is a collection of connected finite state machines Subtypes of cellular automata Graph Grid Subdivision Synchronized
- 32. Whatisacellularautomata: Basically a Cellular automata is a collection of connected finite state machines Subtypes of cellular automata Graph Grid Subdivision Synchronized Cells update at the same time based on the previous state
- 33. Whatisacellularautomata: Basically a Cellular automata is a collection of connected finite state machines Subtypes of cellular automata Graph Grid Subdivision Synchronized Convergent Does the automata settle down for all starting states
- 34. Whatisacellularautomata: The Most famous cellular is Conway’s Game of Life epic game of life
- 35. Whatispathfinding: Path finding is the simply finding one or more optimal routes between two or more points while avoiding obstacles
- 36. Whatispathfinding: Path finding is the simply finding one or more optimal routes between two or more points while avoiding obstacles Used in:
- 37. Whatispathfinding: Path finding is the simply finding one or more optimal route between two or more points while avoiding obstacles Used in: Design (circuit boards, chips, plumbing)
- 38. Whatispathfinding: Path finding is the simply finding one or more optimal route between two or more points while avoiding obstacles Used in: Design (circuit boards, chips, plumbing) Analysis (critical path)
- 39. Whatispathfinding: Path finding is the simply finding one or more optimal route between two or more points while avoiding obstacles Used in: Design (circuit boards, chips, plumbing) Analysis (critical path) Entertainment (goal seeking)
- 41. Otherapproaches topathfinding: Backtracking also known as depth first
- 42. Otherapproaches topathfinding: Backtracking also known as depth first Basically at each branch you “remember” where you were, and which branch you took
- 43. Otherapproaches topathfinding: Backtracking also known as depth first Basically at each branch you “remember” where you were, and which branch you took When you reach a dead end you go back to the last branch and take a different path
- 44. Otherapproaches topathfinding: Backtracking also known as depth first Basically at each branch you “remember” where you were, and which branch you took When you reach a dead end you go back to the last branch and take a different path If the maze has loops or “cycles” depth first can end up going in circles
- 45. Otherapproaches topathfinding: Backtracking also known as depth first Basically at each branch you “remember” where you were, and which branch you took When you reach a dead end you go back to the last branch and take a different path If the maze has loops or “cycles” depth first can end up going in circles This can be prevented by remembering everywhere you’ve been
- 46. Otherapproaches topathfinding: Backtracking also known as depth first Basically at each branch you “remember” where you were, and which branch you took When you reach a dead end you go back to the last branch and take a different path If the maze has loops or “cycles” depth first can end up going in circles Prevented by remembering everywhere you’ve been Easy to implement recursively
- 47. Otherapproaches topathfinding: Backtracking also depth known first
- 48. Otherapproaches topathfinding: Backtracking also known as depth first
- 49. Otherapproaches topathfinding: Backtracking also known as depth first
- 50. Otherapproaches topathfinding: Backtracking also known as depth first
- 51. Otherapproaches topathfinding: Backtracking also known as depth first Breadth first
- 52. Otherapproaches topathfinding: Backtracking also known as depth first Breadth first Again remembering each branch
- 53. Otherapproaches topathfinding: Backtracking also known as depth first Breadth first Again remembering each branch Except at each new intersection, go back to the untried path closest to the starting point
- 54. Otherapproaches topathfinding: Backtracking also known as depth first Breadth first
- 55. Otherapproaches topathfinding: Backtracking also known as depth first Breadth first
- 56. Otherapproaches topathfinding: Backtracking also known as depth first Breadth first
- 57. Otherapproaches topathfinding: Backtracking also known as depth first Breadth first
- 58. Otherapproaches topathfinding: Backtracking also known as depth first Breadth first
- 59. Otherapproaches topathfinding: Backtracking also known as depth first Breadth first
- 60. Otherapproaches topathfinding: Backtracking also known as depth first Breadth first
- 61. Otherapproaches topathfinding: Backtracking also known as depth first Breadth first A* (A star) At each intersection select the “best” untried path (based on a heuristic)
- 62. Otherapproaches topathfinding: A* (A star)
- 63. Otherapproaches topathfinding: A* (A star)
- 64. Otherapproaches topathfinding: A* (A star)
- 65. Otherapproaches topathfinding: A* (A star)
- 67. Shortcomingsofexisting methods: They require both a start and endpoint
- 68. Shortcomingsofexisting methods: They require both a start and endpoint Potentially slow if the maze is large or there are many entities finding paths at the same time
- 69. Shortcomingsofexisting methods: They require both a start and endpoint Potentially slow if the maze is large or there are many entities finding paths at the same time Each entity has a separate path multiplying the amount of memory needed by the number of entities
- 70. Shortcomingsofexisting methods: They require both a start and endpoint Potentially slow if the maze is large or there are many entities finding paths at the same time Each entity has a separate path multiplying the amount of memory needed by the number of entities Not incremental, partial solutions don’t lead to meaningful behavior
- 71. Shortcomingsofexisting methods: They require both a start and endpoint Potentially slow if the maze is large or there are many entities finding paths at the same time Each entity has a separate path multiplying the amount of memory needed by the number of entities Not incremental, partial solutions partial solutions don’t lead to meaningful behavior Not easily distributed
- 72. Shortcomingsofexisting methods: They require both a start and endpoint Potentially slow if the maze is large or there are many entities finding paths at the same time Each entity has a separate path multiplying the amount of memory needed by the number of entities Not incremental, partial solutions partial solutions don’t lead to meaningful behavior Not easily distributed each entity requires a large amount of information
- 73. Whyanewmethod?:
- 74. Whyanewmethod?: Programmers love to reinvent the wheel
- 75. Whyanewmethod?: Programmers love to reinvent the wheel The new algorithm might be better
- 76. Whyanewmethod?: Programmers love to reinvent the wheel The new algorithm might be better To address shortcomings in existing methods
- 77. Whyanewmethod?: Programmers love to reinvent the wheel The new algorithm might be better To address shortcomings in existing methods To learn something
- 78. Whyanewmethod?: Programmers love to reinvent the wheel The new algorithm might be better To address shortcomings in existing methods To learn something (life long learning is important)
- 80. Howdoesthismethodwork?: The states of the automata are as follows
- 81. Howdoesthismethodwork?: The states of the automata are as follows: ‘W’ the cell is a wall
- 82. Howdoesthismethodwork?: The states of the automata are as follows: ‘W’ the cell is a wall ‘G’ the cell is a goal (there can be multiple goals)
- 83. Howdoesthismethodwork?: The states of the automata are as follows: ‘W’ the cell is a wall ‘G’ the cell is a goal 1…10,000 the cell is passable
- 84. Howdoesthismethodwork?: The states of the automata are as follows: ‘W’ the cell is a wall ‘G’ the cell is a goal 1…10,000 the cell is passable The transitions are:
- 85. Howdoesthismethodwork?: The states of the automata are as follows: ‘W’ the cell is a wall ‘G’ the cell is a goal 1…10,000 the cell is passable The transitions are: ‘W’ -> ‘W’ Walls don’t change
- 86. Howdoesthismethodwork?: The states of the automata are as follows: ‘W’ the cell is a wall ‘G’ the cell is a goal 1…10,000 the cell is passable The transitions are: ‘W’ -> ‘W’ ‘G’ -> ‘G’ Goals don’t change
- 87. Howdoesthismethodwork?: The states of the automata are as follows: ‘W’ the cell is a wall ‘G’ the cell is a goal 1…10,000 the cell is passable The transitions are: ‘W’ -> ‘W’ ‘G’ -> ‘G’ 1…10,000 -> one more than its lowest value neighbor. Where ‘G’ has a value of zero
- 88. Howdoesthismethodwork?: The passages are initialized to a random passage value (in the demo initialized to 1 for clarity)
- 89. Howdoesthismethodwork?: The passages are initialized to a random passage value The walls are initialized to ‘W’
- 90. Howdoesthismethodwork?: The passages are initialized to a random passage value The walls are initialized to ‘W’ The goals are initialized to ‘G’
- 91. Howdoesthismethodwork?: The passages are initialized to a random passage value The walls are initialized to ‘W’ The goals are initialized to ‘G’ The automata is stepped either synchronously or asynchronously
- 92. Howdoesthismethodwork?: The passages are initialized to a random passage value The walls are initialized to ‘W’ The goals are initialized to ‘G’ The automata is stepped either synchronously or asynchronously Each entity can simply move to a neighboring cell with a lower value, going “downhill” to player
- 93. Howdoesthismethodwork?: A simple example W W W W W W W G 9 7 1 W W W W W W W
- 94. Howdoesthismethodwork?: A simple example W W W W W W W G 1 2 8 W W W W W W W
- 95. Howdoesthismethodwork?: A simple example W W W W W W W G 1 2 3 W W W W W W W
- 96. Howdoesthismethodwork?: A more complicated example W W W W W W W 1 9 7 1 W W 7 W 5 W W W 8 5 3 G W W W W W W W
- 97. Howdoesthismethodwork?: A more complicated example W W W W W W W 8 2 2 8 W W 2 W 4 W W W 6 4 1 G W W W W W W W
- 98. Howdoesthismethodwork?: A more complicated example W W W W W W W 3 3 3 3 W W 7 W 2 W W W 5 2 1 G W W W W W W W
- 99. Howdoesthismethodwork?: A more complicated example W W W W W W W 4 4 3 4 W W 4 W 2 W W W 8 2 1 G W W W W W W W
- 100. Howdoesthismethodwork?: A more complicated example W W W W W W W 5 4 3 4 W W 4 W 2 W W W 8 2 1 G W W W W W W W
- 101. Howdoesthismethodwork?: A more complicated example W W W W W W W 5 4 3 4 W W 4 W 2 W W W 8 2 1 G W W W W W W W
- 103. Prosandcons:
- 104. Pros: The cellular automata can be shared by entities
- 105. Pros: The cellular automata can be shared by entities Easily distributed
- 106. Pros: The cellular automata can be shared by entities Easily distributed Each cell only needs to know about its closest neighbors
- 107. Pros: The cellular automata can be shared by entities Easily distributed Each cell only needs to know about its closest neighbors The cells don’t need to update synchronously
- 108. Pros: The cellular automata can be shared by entities Easily distributed Incremental the automata can be iterated between frames
- 109. Pros: The cellular automata can be shared by entities Easily distributed Incremental the automata can be iterated between frames Entities will naturally move out of dead ends even before the path information fully propagates
- 110. Pros: The cellular automata can be shared by entities Easily distributed Incremental the automata can be iterated between frames Fault tolerant
- 111. Pros: The cellular automata can be shared by entities Easily distributed Incremental the automata can be iterated between frames Fault tolerant A passage can be blocked to reflect changes in the maze
- 112. Pros: The cellular automata can be shared by entities Easily distributed Incremental the automata can be iterated between frames Fault tolerant A passage can be blocked to reflect changes in the maze Goals can be moved
- 113. Pros: The cellular automata can be shared by entities Easily distributed Incremental the automata can be iterated between frames Fault tolerant If a passage is blocked, or the goal moves Goals can be moved Continue to use the existing automata as it updates
- 114. Pros: The cellular automata can be shared by entities Easily distributed Incremental the automata can be iterated between frames Fault tolerant If a passage is blocked, or the goal moves Goals can be moved Continue to use the existing automata as it updates
- 115. Pros: The cellular automata can be shared by entities Easily distributed Incremental the automata can be iterated between frames Fault tolerant If a passage is blocked, or the goal moves Continue to use the existing automata as it updates Unreachable areas are easily detected
- 116. Cons:
- 117. Cons: Requires enough memory to hold the search space
- 118. Cons: Requires enough memory to hold the search space For a single entity takes more processing than other methods
- 119. Inclosing: This Cellular Automata provides an incremental, fault tolerant, performant pathfinding solution
- 120. References: Ascani, E (2011, October 4). Epic Game of Life. Retrieved April 4, 2016, from https://www.youtube.com/watch?v=C2vgICfQawE Codd, E. F. (1968). Cellular automata [Http://dl.acm.org/citation.cfm?id=1098682]. New York: Academic Press. Retrieved April 4, 2016. DeAngelis, M. (2016, February 29). Cat Maze Disguised as Bookshelves. Retrieved April 4, 2016, from http://www.cluttermagazine.com/news/2016/02/cat-maze-disguised-bookshelves Gardner, M. (1983). Wheels, life, and other mathematical amusements (Chp 20-22). New York: W.H. Freeman. Levy, S. (1993). Artificial life: A report from the frontier where computers meet biology. New York: Vintage Books. Pajot, T. (n.d.). Printed Circuit Board. Retrieved April 4, 2016, from http://www.123rf.com/photo_10607345_printed-circuit-board.html