1. Cellular Automata: Life with Simple Rules
Sharks and Fish:
Predator/Prey Relationships
Bill Madden, Nancy Ricca and Jonathan Rizzo
Graduate Students, Computer Science Department
Research Project using Department’s 20-CPU Cluster

2. Overview
Cellular automata can be used to model complex systems using simple rules.
Key features*
divide problem space into cells
each cell can be in one of several finite states
cells are affected by neighbors according to rules
all cells are affected simultaneously in a generation
rules are reapplied over many generations
*Adapted from: Wilkinson,B and M. Allen (1999): Parallel Programming 2nd Edition, NJ, Pearson Prentice Hall, p189 2

3. Overview This project models a predator/prey relationship
Begins with a randomly distributed population of fish, sharks, and empty cells in a 1000x2000 cell grid (2 million cells)
Initially,
50% of the cells are occupied by fish
25% are occupied by sharks
25% are empty 3

4. Here’s the number 2 million
Fish: red; sharks: yellow; empty: black 4

5. Rules A dozen or so rules describe life in each cell:
birth, longevity and death of a fish or shark
breeding of fish and sharks
over- and under-population
fish/shark interaction
Important: what happens in each cell is determined only by rules that apply locally, yet which often yield long-term large-scale patterns. 5

6. Do a LOT of computation! Apply a dozen rules to each cell
Do this for 2 million cells in the grid
Do this for 20,000 generations
Well over a trillion calculations per run!
Do this as quickly as you can 6

7. Do a LOT of computation!
We used a 20-CPU cluster in the Computer Science Department (Galaxy)
‘Gal’ is the smaller of two clusters run by the Department (larger one has 64 CPUs)
15x faster than a single PC
Longest runs still took about 45 minutes
GO PARALLEL !!! 7

8. Rules in detail: Initial Conditions
Initially cells contain fish, sharks or are empty
Empty cells = 0 (black pixel)
Fish = 1 (red pixel)
Sharks = –1 (yellow pixel) 8

9. Rules in detail: Breeding Rule
Breeding rule: if the current cell is empty
If there are >= 4 neighbors of one species, and >= 3 of them are of breeding age,
Fish breeding age >= 2,
Shark breeding age >=3,
and there are <4 of the other species:
then create a species of that type
+1= baby fish (age = 1 at birth)
-1 = baby shark (age = |-1| at birth) 9

10. Breeding Rule: Before
EMPTY 10

11. Breeding Rule: After 11

12. Rules in Detail: Fish Rules
If the current cell contains a fish:
Fish live for 10 generations
If >=5 neighbors are sharks, fish dies (shark food)
If all 8 neighbors are fish, fish dies (overpopulation)
If a fish does not die, increment age 12

13. Rules in Detail: Shark Rules
If the current cell contains a shark:
Sharks live for 20 generations
If >=6 neighbors are sharks and fish neighbors =0, the shark dies (starvation)
A shark has a 1/32 (.031) chance of dying due to random causes
If a shark does not die, increment age 13

14. Shark Random Death: Before
I Sure Hope that the
random number
chosen is >.031 14

15. Shark Random Death: After
YES IT IS!!!
I LIVE  15

16. Programming logic Use 2-dimensional array to represent grid
At any one (x, y) position, value is:
Positive integer (fish present)
Negative integer (shark present)
Zero (empty cell)
Absolute value of cell is age 16

17. Sample Code (C++): Breeding17

18. Parallelism A single CPU has to do it all:
Applies rules to first cell in array
Repeats rules for each successive cell in array
After 2 millionth cell is processed, array is updated
One generation has passed
Repeat this process for many generations
Every 100 generations or so, convert array to red, yellow and black pixels and send results to screen 18

19. Parallelism How to split the work among 20 CPUs
1 CPU acts as Master (has copy of whole array)
18 CPUs act as Slaves (handle parts of the array)
1 CPU takes care of screen updates
Problem: communication issue concerning cells along array boundaries among slaves 19

20. Send Right Boundary Values
Subdivide grid into 18 vertical slices
Each slice has a left boundary and a right boundary
Set the left boundary of the left-most slice to a preset value (we used 0=empty)
Do same for right boundary of right-most slice (and top and bottom of all slices)
Each slave sends its boundary results to its left and right neighbor slaves
Each slave receives boundary information from its neighbor slaves
At intervals, all slaves update the master CPU 20

21. Receive Left Boundary Values21

22. Send Left Boundary Values22

23. Receive Right Boundary Values23

24. Send Right Boundary Values24

25. Receive Left Boundary Values25

26. Send Left Boundary Values26

27. Receive Right Boundary Values27

28. At intervals, update the master CPU
has copy of entire array 28

29. MPI Classes
‘Gal’ (the 20-CPU cluster we used) has special enhancements to C++, called MPI Classes, which handle such boundary communication issues
Other than that, each slave processes its portion of the array much as a single CPU would process the whole array except, of course, they each have only 1/18th of the problem to solve! 29

30. Results
Next several screens show behavior over a span of 10,000+ generations (about 25 minutes on Gal) 30

31. Generation: 0 31

32. Generation: 100 32

33. Generation: 500 33

34. Generation: 1,000 34

35. Generation: 2,000 35

36. Generation: 4,000 36

37. Generation: 8,000 37

38. Generation: 10,500 38

39. Long-term trends
Borders tended to ‘harden’ along vertical, horizontal and diagonal lines
Borders of empty cells form between like species
Clumps of fish tend to coalesce and form convex shapes or ‘communities’ 39

40. Variations of Initial Conditions
Still using randomly distributed populations:
Medium-sized population. Fish/sharks occupy: 1/16th of total grid Fish: 62,703; Sharks: 31,301
Very small population. Fish/sharks occupy: 1/800th of total grid Initial population: Fish: 1,298; Sharks: 609 40

41. Medium-sized population (1/16 of grid)
Generation 100
1000
2000
4000
8000 41

42. Very Small Populations
Random placement of very small populations can favor one species over another
Fish favored: sharks die out
Sharks favored: sharks predominate, but fish survive in stable small numbers 42

43. Very Small Populations
Gen. 100
1500
4000
6000
8000
10,000
12,000
14,000
Ultimate welfare of sharks depends on initial random
placement of fish and sharks 43

44. Very small populations
Fish can live in stable isolated communities as small as 20-30
A community of less than 200 sharks tends not to be viable 44

45. Parallel Performance
Parallel processing suggests speedup of close to 18 is possible
Our results: 15x speedup
Reason: communication overhead among slaves and between slaves and master
Communication overhead becomes much worse if results are communicated more often 45

46. Speed-up 46

47. Communication Overhead47

48. Acknowledgements
Bill Madden, Nancy Ricca and Jonathan Rizzo, Graduate Students, Computer Science Department, Montclair State University
Dr. Roman Zaritski, Professor, Computer Science Department, Montclair State University
Galaxy: 20-CPU cluster in Computer Science Department, Montclair State University 48

49. Parallel Processing Laboratory
This presentation is available on-line at:
The web site above also hosts a number of other interesting parallel computing projects and is the on-line “home” of the Computer Science Department’s Parallel Processing Laboratory.
GO PARALLEL !!! 49