Questions for Week 11.  Complex Systems I

 

This tutorial uses NetLogo to explore cellular automata.

 

Part A. 1D Cellular Automata

Explore the 1D models in the File Menu à  Models Library/Computer Science/Cellular Automata CAs 110, 90, 230, 30 to get a feel for the variation in the 1D CAs. Read the “description” tabs for each model to find out what is interesting about each pattern.
Use the general model Cellular Automata 1D, to answer question 1 below.
Use the extended version from File Menu à  Models Library/Unverified Models/ Cellular Automata 1Dchange to answer question 2. If you have loaded NetLogo on your own machine, copy this model from the directory at  www.itee.uq.edu.au/~cogs2010/NetLogo/models/Unverified Models

 

  1. Wolfram claimed to find four classes of patterns: simple, repetitive, chaotic and complex.
    Find two example CAs of each of these classes. List their numbers (in binary or in decimal; ie 00000000 to 11111111 or  0 to 255) and describe the behaviours of each class.
  2. For each of the patterns, change one bit in the initial CA and observe whether the changes

a.        always die out

b.       are constrained to a finite number of patches

c.        always propagate to all patches

d.       propagate in a limited way that may give rise to higher structures

Summarise your results.

 

Part B. 2D Cellular Automata: The Game of Life

For background to CAs, read the introduction to the Game of Life at http://life.csu.edu.au/complex/tutorials/tutorial1.html

 

Explore the behaviours of the Game of Life using the NetLogo version (File Menu à  Models Library/Computer Science/Cellular Automata/Life)

Try out some of the interesting patterns, such as the R pentomino pattern:

      xx

     xx

      x

What happens when other cells are initially occupied?

Some other interesting patterns to try include:

 

   *       *      **        *         

    **      *     **         *       

  **      ***            *   *                

    *                     ****    

 

 Clock  Glider  Block  Spaceship

 

 

Question 3.

a.        Find another recurring shape other than gliders and blinkers and those given above.

b.       Explain what happens at different density levels.

c.        Is there a "critical density" - one at which simple repetitive changes stop and chaotic or eternal motion begins?

 

 

For interest only: The following web page lists for a variety of implementations

http://www-2.cs.cmu.edu/afs/cs/project/ai-repository/ai/areas/alife/systems/life/0.html