cellular automata for pathfinding

Cellular Automata for Pathfinding

A Fault tolerant, Parallelizable incremental approach for real time environments

Steve Wilson

Cellular Automata for pathfinding:Over view:

What is a cellular automataHow it is related to other automata

What is path finding Other approaches to pathfindingWhy a new method ?The cellular approachPros and Cons of using cellular automata

Cellular Automata for pathfinding:What is a cellular automata:

Types of “automata”

Cellular Automata for pathfinding:What is a cellular automata:

Types of “automata” or “machines”

Cellular Automata for pathfinding:What is a cellular automata:

Types of automataFinite state machine

Cellular Automata for pathfinding:What is a cellular automata:

Types of automataFinite state machine

One or more states

Cellular Automata for pathfinding:What is a cellular automata:

Types of automataFinite state machine

One or more statesTransition rules

Cellular Automata for pathfinding:What is a cellular automata:

Types of automataFinite state machine

One or more statesTransition rules Input

Cellular Automata for pathfinding:What is a cellular automata:

Types of automataFinite state machinePush down automata

Cellular Automata for pathfinding:What is a cellular automata:

Types of automataFinite state machinePush down automata

One or more states

Cellular Automata for pathfinding:What is a cellular automata:

Types of automataFinite state machinePush down automata

One or more statesTransition rules

Cellular Automata for pathfinding:What is a cellular automata:

Types of automataFinite state machinePush down automata

One or more statesTransition rulesInput

Cellular Automata for pathfinding:What is a cellular automata:

Types of automataFinite state machinePush down automata

One or more statesTransition rulesInputStack

Cellular Automata for pathfinding:What is a cellular automata:

Types of automataFinite state machinePush down automata

Turing machine

Cellular Automata for pathfinding:What is a cellular automata:

Types of automataFinite state machinePush down automata

Turing machineOne or more states

Cellular Automata for pathfinding:What is a cellular automata:

Types of automataFinite state machinePush down automata

Turing machineOne or more statesTransition rules

Cellular Automata for pathfinding:What is a cellular automata:

Types of automataFinite state machinePush down automata

Turing machineOne or more statesTransition rulesTape

Cellular Automata for pathfinding:What is a cellular automata:

Types of automataFinite state machinePush down automataTuring machine

Cellular Automata

Cellular Automata for pathfinding:What is a cellular automata:

Types of automataFinite state machinePush down automataTuring machine

Cellular AutomataTwo or more states

Cellular Automata for pathfinding:What is a cellular automata:

Types of automataFinite state machinePush down automataTuring machine

Cellular AutomataTwo or more statesTransition rules

Cellular Automata for pathfinding:What is a cellular automata:

Types of automataFinite state machinePush down automataTuring machine

Cellular AutomataTwo or more statesTransition rulesNeighbor states

Cellular Automata for pathfinding:What is a cellular automata:

Basically

Cellular Automata for pathfinding:What is a cellular automata:

Basically a Cellular automata is a collection of connected finite state machines

Cellular Automata for pathfinding:What is a cellular automata:

Basically a Cellular automata is a collection of connected finite state machinesSubtypes of cellular automata

Cellular Automata for pathfinding:What is a cellular automata:

Basically a Cellular automata is a collection of connected finite state machinesSubtypes of cellular automata

Graph

Cellular Automata for pathfinding:What is a cellular automata:

Basically a Cellular automata is a collection of connected finite state machinesSubtypes of cellular automata

GraphCells are connected by “edges”

Cellular Automata for pathfinding:What is a cellular automata:

Basically a Cellular automata is a collection of connected finite state machinesSubtypes of cellular automata

GraphGrid

Cellular Automata for pathfinding:What is a cellular automata:

Basically a Cellular automata is a collection of connected finite state machinesSubtypes of cellular automata

GraphGrid

Cells are arranged uniformly in a patternand connected spatially

Cellular Automata for pathfinding:What is a cellular automata:

Basically a Cellular automata is a collection of connected finite state machinesSubtypes of cellular automata

GraphGridSubdivision

Cellular Automata for pathfinding:What is a cellular automata:

Basically a Cellular automata is a collection of connected finite state machinesSubtypes of cellular automata

GraphGridSubdivision

Used extensively in modeling, cells are connected spatially in a non-uniform manner

Cellular Automata for pathfinding:What is a cellular automata:

Basically a Cellular automata is a collection of connected finite state machinesSubtypes of cellular automata

GraphGridSubdivisionSynchronized

Cellular Automata for pathfinding:What is a cellular automata:

Basically a Cellular automata is a collection of connected finite state machinesSubtypes of cellular automata

GraphGridSubdivisionSynchronized

Cells update at the same time based on the previous state

Cellular Automata for pathfinding:What is a cellular automata:

Basically a Cellular automata is a collection of connected finite state machinesSubtypes of cellular automata

GraphGridSubdivisionSynchronizedConvergent

Does the automata settle down for all starting states

Cellular Automata for pathfinding:What is a cellular automata:

The Most famous cellular is Conway’s Game of Life

epic game of life

Cellular Automata for pathfinding:What is path finding:

Path finding is the simply finding one or more optimal routes between two or more points while avoiding obstacles

Cellular Automata for pathfinding:What is path finding:

Path finding is the simply finding one or more optimal routes between two or more points while avoiding obstaclesUsed in:

Cellular Automata for pathfinding:What is path finding:

Path finding is the simply finding one or more optimal route between two or more points while avoiding obstaclesUsed in:

Design (circuit boards, chips, plumbing)

Cellular Automata for pathfinding:What is path finding:

Path finding is the simply finding one or more optimal route between two or more points while avoiding obstaclesUsed in:

Design (circuit boards, chips, plumbing) Analysis (critical path)

Cellular Automata for pathfinding:What is path finding:

Path finding is the simply finding one or more optimal route between two or more points while avoiding obstaclesUsed in:

Design (circuit boards, chips, plumbing) Analysis (critical path)Entertainment (goal seeking)

Cellular Automata for pathfinding:Other approaches to pathfinding:

Cellular Automata for pathfinding:Other approaches to pathfinding:

Backtracking also known as depth first

Cellular Automata for pathfinding:Other approaches to pathfinding:

Backtracking also known as depth firstBasically at each branch you “remember” where you were, and which branch you took

Cellular Automata for pathfinding:Other approaches to pathfinding:

Backtracking also known as depth firstBasically at each branch you “remember” where you were, and which branch you tookWhen you reach a dead end you go back to the last branch and take a different path

Cellular Automata for pathfinding:Other approaches to pathfinding:

Backtracking also known as depth firstBasically at each branch you “remember” where you were, and which branch you tookWhen you reach a dead end you go back to the last branch and take a different pathIf the maze has loops or “cycles” depth first can end up going in circles

Cellular Automata for pathfinding:Other approaches to pathfinding:

Backtracking also known as depth firstBasically at each branch you “remember” where you were, and which branch you tookWhen you reach a dead end you go back to the last branch and take a different pathIf the maze has loops or “cycles” depth first can end up going in circlesThis can be prevented by remembering everywhere you’ve been

Cellular Automata for pathfinding:Other approaches to pathfinding:

Backtracking also known as depth firstBasically at each branch you “remember” where you were, and which branch you tookWhen you reach a dead end you go back to the last branch and take a different pathIf the maze has loops or “cycles” depth first can end up going in circlesPrevented by remembering everywhere you’ve beenEasy to implement recursively

Cellular Automata for pathfinding:Other approaches to pathfinding:

Backtracking also depth known first

Cellular Automata for pathfinding:Other approaches to pathfinding:

Backtracking also known as depth first

Cellular Automata for pathfinding:Other approaches to pathfinding:

Backtracking also known as depth first

Cellular Automata for pathfinding:Other approaches to pathfinding:

Backtracking also known as depth first

Cellular Automata for pathfinding:Other approaches to pathfinding:

Backtracking also known as depth firstBreadth first

Cellular Automata for pathfinding:Other approaches to pathfinding:

Backtracking also known as depth firstBreadth first

Again remembering each branch

Cellular Automata for pathfinding:Other approaches to pathfinding:

Backtracking also known as depth firstBreadth first

Again remembering each branchExcept at each new intersection, go back to the untried path closest to the starting point

Cellular Automata for pathfinding:Other approaches to pathfinding:

Backtracking also known as depth firstBreadth first

Cellular Automata for pathfinding:Other approaches to pathfinding:

Backtracking also known as depth firstBreadth first

Cellular Automata for pathfinding:Other approaches to pathfinding:

Backtracking also known as depth firstBreadth first

Cellular Automata for pathfinding:Other approaches to pathfinding:

Backtracking also known as depth firstBreadth first

Cellular Automata for pathfinding:Other approaches to pathfinding:

Backtracking also known as depth firstBreadth first

Cellular Automata for pathfinding:Other approaches to pathfinding:

Backtracking also known as depth firstBreadth first

Cellular Automata for pathfinding:Other approaches to pathfinding:

Backtracking also known as depth firstBreadth first

Cellular Automata for pathfinding:Other approaches to pathfinding:

Backtracking also known as depth firstBreadth firstA* (A star)

At each intersection select the “best” untried path (based on a heuristic)

Cellular Automata for pathfinding:Other approaches to pathfinding:

A* (A star)

Cellular Automata for pathfinding:Other approaches to pathfinding:

A* (A star)

Cellular Automata for pathfinding:Other approaches to pathfinding:

A* (A star)

Cellular Automata for pathfinding:Other approaches to pathfinding:

A* (A star)

Cellular Automata for pathfinding:Shortcomings of existing methods:

Cellular Automata for pathfinding:Shortcomings of existing methods:

They require both a start and endpoint

Cellular Automata for pathfinding:Shortcomings of existing methods:

They require both a start and endpointPotentially slow if the maze is large or there are many entities finding paths at the same time

Cellular Automata for pathfinding:Shortcomings of existing methods:

They require both a start and endpointPotentially slow if the maze is large or there are many entities finding paths at the same timeEach entity has a separate path multiplying the amount of memory needed by the number of entities

Cellular Automata for pathfinding:Shortcomings of existing methods:

They require both a start and endpointPotentially slow if the maze is large or there are many entities finding paths at the same timeEach entity has a separate path multiplying the amount of memory needed by the number of entitiesNot incremental, partial solutions don’t lead to meaningful behavior

Cellular Automata for pathfinding:Shortcomings of existing methods:

They require both a start and endpointPotentially slow if the maze is large or there are many entities finding paths at the same timeEach entity has a separate path multiplying the amount of memory needed by the number of entitiesNot incremental, partial solutions partial solutions don’t lead to meaningful behaviorNot easily distributed

Cellular Automata for pathfinding:Shortcomings of existing methods:

They require both a start and endpointPotentially slow if the maze is large or there are many entities finding paths at the same timeEach entity has a separate path multiplying the amount of memory needed by the number of entitiesNot incremental, partial solutions partial solutions don’t lead to meaningful behaviorNot easily distributed each entity requires a large amount of information

Cellular Automata for pathfinding:Why a new method?:

Cellular Automata for pathfinding:Why a new method?:

Programmers love to reinvent the wheel

Cellular Automata for pathfinding:Why a new method?:

Programmers love to reinvent the wheelThe new algorithm might be better

Cellular Automata for pathfinding:Why a new method?:

Programmers love to reinvent the wheelThe new algorithm might be betterTo address shortcomings in existing methods

Cellular Automata for pathfinding:Why a new method?:

Programmers love to reinvent the wheelThe new algorithm might be betterTo address shortcomings in existing methodsTo learn something

Cellular Automata for pathfinding:Why a new method?:

Programmers love to reinvent the wheelThe new algorithm might be betterTo address shortcomings in existing methodsTo learn something (life long learning is important)

Cellular Automata for pathfinding:How does this method work?:

Cellular Automata for pathfinding:How does this method work?:

The states of the automata are as follows

Cellular Automata for pathfinding:How does this method work?:

The states of the automata are as follows:‘W’ the cell is a wall

Cellular Automata for pathfinding:How does this method work?:

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)

Cellular Automata for pathfinding:How does this method work?:

The states of the automata are as follows:‘W’ the cell is a wall‘G’ the cell is a goal1…10,000 the cell is passable

Cellular Automata for pathfinding:How does this method work?:

The states of the automata are as follows:‘W’ the cell is a wall‘G’ the cell is a goal1…10,000 the cell is passable

The transitions are:

Cellular Automata for pathfinding:How does this method work?:

The states of the automata are as follows:‘W’ the cell is a wall‘G’ the cell is a goal1…10,000 the cell is passable

The transitions are:‘W’ -> ‘W’ Walls don’t change

Cellular Automata for pathfinding:How does this method work?:

The states of the automata are as follows:‘W’ the cell is a wall‘G’ the cell is a goal1…10,000 the cell is passable

The transitions are:‘W’ -> ‘W’‘G’ -> ‘G’ Goals don’t change

Cellular Automata for pathfinding:How does this method work?:

The states of the automata are as follows:‘W’ the cell is a wall‘G’ the cell is a goal1…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

Cellular Automata for pathfinding:How does this method work?:

The passages are initialized to a random passage value (in the demo initialized to 1 for clarity)

Cellular Automata for pathfinding:How does this method work?:

The passages are initialized to a random passage value The walls are initialized to ‘W’

Cellular Automata for pathfinding:How does this method work?:

The passages are initialized to a random passage value The walls are initialized to ‘W’The goals are initialized to ‘G’

Cellular Automata for pathfinding:How does this method work?:

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

Cellular Automata for pathfinding:How does this method work?:

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

Cellular Automata for pathfinding:How does this method work?:

A simple example

W W W W W WW G 9 7 1 WW W W W W W

Cellular Automata for pathfinding:How does this method work?:

A simple example

W W W W W WW G 1 2 8 WW W W W W W

Cellular Automata for pathfinding:How does this method work?:

A simple example

W W W W W WW G 1 2 3 WW W W W W W

Cellular Automata for pathfinding:How does this method work?:

A more complicated example

W W W W W WW 1 9 7 1 WW 7 W 5 W WW 8 5 3 G WW W W W W W

Cellular Automata for pathfinding:How does this method work?:

A more complicated example

W W W W W WW 8 2 2 8 WW 2 W 4 W WW 6 4 1 G WW W W W W W

Cellular Automata for pathfinding:How does this method work?:

A more complicated example

W W W W W WW 3 3 3 3 WW 7 W 2 W WW 5 2 1 G WW W W W W W

Cellular Automata for pathfinding:How does this method work?:

A more complicated example

W W W W W WW 4 4 3 4 WW 4 W 2 W WW 8 2 1 G WW W W W W W

Cellular Automata for pathfinding:How does this method work?:

A more complicated example

W W W W W WW 5 4 3 4 WW 4 W 2 W WW 8 2 1 G WW W W W W W

Cellular Automata for pathfinding:How does this method work?:

A more complicated example

W W W W W WW 5 4 3 4 WW 4 W 2 W WW 8 2 1 G WW W W W W W

Cellular Automata for pathfinding:How does this method work?:

Demo Here:

Cellular Automata for pathfinding:Pros and cons:

Cellular Automata for pathfinding:Pros :

The cellular automata can be shared by entities

Cellular Automata for pathfinding:Pros:

The cellular automata can be shared by entitiesEasily distributed

Cellular Automata for pathfinding:Pros:

The cellular automata can be shared by entitiesEasily distributed

Each cell only needs to know about its closest neighbors

Cellular Automata for pathfinding:Pros:

The cellular automata can be shared by entitiesEasily distributed

Each cell only needs to know about its closest neighborsThe cells don’t need to update synchronously

Cellular Automata for pathfinding:Pros:

The cellular automata can be shared by entitiesEasily distributedIncremental the automata can be iterated between frames

Cellular Automata for pathfinding:Pros:

The cellular automata can be shared by entitiesEasily distributedIncremental the automata can be iterated between frames

Entities will naturally move out of dead ends even before the path information fully propagates

Cellular Automata for pathfinding:Pros:

The cellular automata can be shared by entitiesEasily distributedIncremental the automata can be iterated between framesFault tolerant

Cellular Automata for pathfinding:Pros:

The cellular automata can be shared by entitiesEasily distributedIncremental the automata can be iterated between framesFault tolerant

A passage can be blocked to reflect changes in the maze

Cellular Automata for pathfinding:Pros:

The cellular automata can be shared by entitiesEasily distributedIncremental the automata can be iterated between framesFault tolerant

A passage can be blocked to reflect changes in the mazeGoals can be moved

Cellular Automata for pathfinding:Pros:

The cellular automata can be shared by entitiesEasily distributedIncremental the automata can be iterated between framesFault tolerant

If a passage is blocked, or the goal movesGoals can be movedContinue to use the existing automata as it updates

Cellular Automata for pathfinding:Pros:

The cellular automata can be shared by entitiesEasily distributedIncremental the automata can be iterated between framesFault tolerant

If a passage is blocked, or the goal movesGoals can be movedContinue to use the existing automata as it updates

Cellular Automata for pathfinding:Pros:

The cellular automata can be shared by entitiesEasily distributedIncremental the automata can be iterated between framesFault tolerant

If a passage is blocked, or the goal movesContinue to use the existing automata as it updates

Unreachable areas are easily detected

Cellular Automata for pathfinding:Cons:

Cellular Automata for pathfinding:Cons:

Requires enough memory to hold the search space

Cellular Automata for pathfinding:Cons:

Requires enough memory to hold the search spaceFor a single entity takes more processing than other methods

Cellular Automata for pathfinding:In closing:

This Cellular Automata provides an incremental, fault tolerant, performant pathfinding solution

Cellular Automata for pathfinding: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