This document describes a cellular automata approach to pathfinding. It begins by defining types of automata and explaining that a cellular automata is a collection of connected finite state machines. It then discusses existing pathfinding algorithms like backtracking, breadth-first search, and A* and their shortcomings. The document proposes a new cellular automata method where passage cells take on values based on their lowest-value neighbors, allowing entities to move downhill towards goals. It provides examples of how this approach works and notes pros like distributed processing and incremental updates.

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

3. Whatisacellularautomata:
Types of “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

22. Whatisacellularautomata:
Basically

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)

40. Otherapproaches topathfinding:

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)

66. Shortcomingsofexisting methods:

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)

79. Howdoesthismethodwork?:

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

102. Howdoesthismethodwork?:
Demo Here:

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