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. -------------------------------------------------------------------------- Files and Installation -------------------------------------------------------------------------- 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. -------------------------------------------------------------------------- Theory behind Anty World -------------------------------------------------------------------------- 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 ant’s 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 Langton’s 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 it’s 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 it’s 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 it’s step, turn and increment behavior until interrupted by the user or until it walks out of the realm of Anty World. -------------------------------------------------------------------------- References -------------------------------------------------------------------------- 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. -------------------------------------------------------------------------- About the Author -------------------------------------------------------------------------- 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.