                  Anty World Simulation v1.0

                   Written By Adrian Akison
                        August 3, 1994

Anty World is a simple cellular autonoma that has some 
remarkable results.  It simulates an ant who must abide by some 
very simple rules when travelling through its world.  As it 
travels it changes the color of the ground it has been on.  The 
color of the ground also determines how it should turn as it 
travels.  The program comes complete with an intuitive 
interface, a complete help file and it requires Windows 3.0 or 
later.

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Files and Installation
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Main program files:

ANTYSIM.TXT - This file
ANTYSIM.EXE - Windows executable file
ANTYSIM.HLP - Windows help file

Support files and controls:

CMDIALOG.VBX
MH3B200.VBX
MHCM200.VBX
MHRUN300.DLL
PUSHHELP.VBX
not included - VBRUN300.DLL

The support files above are included in the ZIP file and must 
either be in the current directory or in the Windows system 
directory while the program is running.  Additionally, the 
Visual Basic runtime library, VBRUN300.DLL, is required.  For 
space considerations it is not included with these files but is 
available from the SimTel archives, CompuServe and various 
other sources.

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Theory behind Anty World
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Anty World is a very simple cellular automaton.  In it, the 
user gives an ant a set of rules that it must follow.  The 
rules in this world determine how the ant will turn.  The rule 
set that is chosen can result in a multitude of patterns.  They 
can be as simple as a four square box, they can be complex 
patterns, they can be purely chaotic or they can produce a 
combination of patterns.

The realm of the ants world, Anty World, is a grid of colored 
squares.  In this simulation, the ant starts in the middle of a 
grid of black squares.  The ant begins walking and as it leaves 
a square it changes the squares color.  It then examines the 
color of the square it is on and decides whether to turn left 
or right based on this color.  The number of possible colors in 
this simulation is determined by the ants rule string.

The original idea was advanced by Chris Langton of the Sante Fe 
Institute.  His first ant followed the following rule set: 	
If the square is black then color square white and turn right. 	
If the square is white then color square black and turn left. 
This ant is referred to as Langtons Ant.  Although this rule 
set seems extremely simple, it creates a seemingly chaotic 
pattern for the first 10,000 or so steps.  After this, however, 
it creates a pattern that causes the ant to create the same 
pattern again but offset by a few squares.  This leads to an 
infinite number of these patterns being created, each slightly 
offset from and overlapping the previous.  This phenomena has 
been termed highway construction.  This ant can be seen 
working by playing the default rule string in the simulation.

The rule string that can be entered in the main window has the 
following affect on the ant and its world: 	
  1. Anty World consists of as many colors as the string is long. 	
  2. When the ant leaves a square, it increments the color shade. 	
  3. When the color shade is at its highest, the color wraps around 
       to black.
  4. The ant looks at the color that it has just stepped on, call it n. 
  5. If the nth character of the rule string is L then it turns left.
  6. If the nth character of the rule string is R then it turns right. 
The ant will continue its step, turn and increment behavior 
until interrupted by the user or until it walks out of the 
realm of Anty World.

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References
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All information for this program was taken from the following reference:

MATHEMATICAL RECREATIONS.  Ian Stewart in Scientific American, 
  Vol. 271, No. 1, pages 104-107; July 1994.

For completeness, his reference section follows:

WINNING WAYS, VOL 2:  FOR YOUR MATHEMATICAL PLAYS:  GAMES IN 
  PARTICULAR.  Elwyn R. Berlekamp, John H. Conway and Richard K. 
  Guy.  Academic Press, 1982.

COMPUTER RECREATIONS.  A. K. Dewdney in Scientific American, 
  Vol. 261, No. 3, pages 180-183; September 1989 and Vol. 262, 
  No. 3, pages 118-121; March 1990.

MATHEMATICAL ENTERTAINMENTS. Daved Gale in Mathematical 
  Intelligencer, Vol. 15, No. 2, pages 54-55; Spring 1993.

FURTHER ANT-ICS:  TRAJECTORY OF GENERALIZED ANTS.  Jim Propp in 
  Mathematical Intelligencer, Vol. 16, No. 1, pages 37-42; Winter 
  1994.

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About the Author
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Adrian Akison is a computer programmer and analyst for Cobe 
Renal Care in Lakewood, Colorado.  He has a degree in 
mathematics and economics from the University of Southern 
California.  In addition he is a graduate student and the 
University of Colorado.  He can be reached at:

     Internet:       adrian.akison@cobe.com
     CompuServe:     74521,103
     USPS:           Cobe Renal Care
                     1185 Oak St.
                     Lakewood, CO  80203

Feel free to forward any comments or suggestions for 
improvement pertaining to the simulation or help file.

