1. Cellular Automata and Game Design By Pete Strader

2.  Game and Media Design  Procedural Generation  Cellular Automata  Game of Life  Simple state  Sheep vs. Wolves  Mathematical Model  Orcs V.S. Elves Orcs V.S. Elves  Future Work  Sources Topic Points

3.  The development process of CG content  The world  The AI (characters)  The Storyline  Saves time and money Game and Media Design of Video Games

4.  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 Generation Content Generated Algorithmically

5. Generated Examples  Geography  Vegetation  Architecture

6.  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

7. Game of Life John 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

8.  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 Dimension Peter Strader (2013)

9. One Dimension, Two States

10.  Two competing organisms  No longer cells but free moving agents  Predator vs. Prey Predator vs. Prey  Wolves eat sheep  Sheep eat grass Sheep vs. Wolves Where Cellular Automata Meets Random Movement

12. 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)

13. 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

15.  Predator vs. Predator Predator vs. Predator  Both eat each other  Stop when stamina is low Operation Clever Sheep Maniacal laugh …

17. 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

18. Study of the Tie-Line 100 Sheep100 Wolves Wolves25/60 Sheep32/60 Tie3/60 1 Sheep1 Wolf Wolves12/60 Sheep18/60 Tie30/60 1 Wolf1 sheep Wolves11/60 Sheep11/60 Tie38/60

19.  Orcs V.s. Elves 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

20.  Expand on code for battle simulator  Add Reinforcements  Study battle outcomes  Add Tactics Future Work

21. 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) http://procworld.blogspot.com/  Massive Software (2013) Massive Software