cellular automata and game design by pete strader
Post on 28-Dec-2015
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Game and Media Design Procedural
Generation Cellular
Automata Game of Life Simple state
Sheep vs. Wolves Mathematical
Model Orcs V.S. Elves
Future Work Sources
Topic Points
The development process of CG content The world The AI
(characters) The Storyline
Saves time and money
Game and Media Designof Video Games
Used in graphics and AI Fractals
Land Scape Geometry
Purlin Noise Texture
Pseudo-Random Variables
Cellular Automata AI Behavior AKA: Agents, NPC,
or Mobs
Procedural GenerationContent Generated Algorithmically
Method of discrete modeling Demonstrates the
macro in the micro Feedback machine
Standard form A grid of cells States of On/Off Cell relationships
Rules dictate the behavior of cells Ex: Game of Life
Cellular Automata
Game of LifeJohn Conway (1970)
Any live cell with fewer than two live neighbors dies, as if caused by under-population.
Any live cell with two or three live neighbors lives on to the next generation.
Any live cell with more than three live neighbors dies, as if by overcrowding.
Any dead cell with exactly three live neighbors becomes a live cell, as if by reproduction
If a cell has an open space to the right, it propagates to that cell
If a cell has an open space to the left, it lives
Each step follows: Birth Phase Death Phase
Simple One DimensionPeter Strader (2013)
Two competing organisms
No longer cells but free moving agents
Predator vs. Prey Wolves eat sheep
Sheep eat grass
Sheep vs. WolvesWhere Cellular Automata Meets Random Movement
Lotka-Volterra Predator / Prey Model
The model for predator vs. prey
ΔS = α*S-β*S*W
ΔW=ε*S*W-γ*W
Look for the non-trivial steady state, using Jacobean to describe the population plain as stable or unstable.
Non-trivial steady state
J(S,W) = [ ]
Trivial steady state
J(0,0)= [ ]
Eigen values are:
λ = α,-γ
Therefore there exists a system we can model
ΔS = α*S-β*S*W || ΔW=ε*S*W-γ*W
dS/dt = S(α-βW) || dW/dt = W(εS-γ)
dW/dS = W(εS-γ)/ S(α-βW)
S(α-βW)dW = W(εS-γ)dS
(α-βW)(1/W)dW = (εS-γ)(1/S)dS
(α-βW)(1/W)dW - (εS-γ)(1/S)dS = 0
ɸ(S,W) = αLog(W)-βW – εS-γLog(S) = A
Predator vs. Predator
Both eat each other
Stop when stamina is low
Operation Clever Sheep Maniacal laugh …
The model for predator vs. predator
ΔS = -β*S*W
ΔW=-β*S*W
Look for the non-trivial steady state, using Jacobean to describe the population plain.
J(W,S) = [ ]
J(W,0) = [ ] or J(0,S) = [ ]
Therefore our Eigenvalues are:
λ = 0,0
(dW/dS)=(dW/dt)(dS/dt) = (ΔW /ΔS) = 1.
Our point of contention is the one to one tie line
Study of the Tie-Line
100 Sheep
100 Wolves
Wolves 25/60
Sheep 32/60
Tie 3/60
1 Sheep 1 Wolf
Wolves 12/60
Sheep 18/60
Tie 30/60
1 Wolf 1 sheep
Wolves 11/60
Sheep 11/60
Tie 38/60
Orcs V.s. Elves
Visual tracking
Skirmish fighting
Equal chance of
kill Die from over
exhaustion Wants:
Ranged Attacks Flocking/Tactic Reinforcements
Orcs V.s Elves Battle Simulator
Expand on code for battle simulator
Add Reinforcements
Study battle outcomes
Add Tactics
Future Work
Sources Nicholas F. Britton, Essential Mathematical
Biology, Springer (2003), pg. 54 Peigen, Jürgens, and Saupe, Chaos and
Fractals, New Frontiers of Science, Springer (1996), pg. 412
NetLogo 5.0.4, (2013) Miguel Cepero, Procedural World,
http://procworld.blogspot.com/ (2013) Massive Software (2013)
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