UMass Lowell CyberEd
92.419 Computer Algebra with Mathematica
Kenneth M. Levasseur
Department of Mathematical Sciences
University of Massachusetts Lowell
Lowell, MA 01852
Raw Recruits
Subject: Patterns, cellular automata
Introduction: Six young recruits stand in a single line for their first drill session. They face the gruff drill sergeant, who barks out their first order — "Left Face" — and they all react in one second this way:
Not bad - almost all of them get it right! However, each is very nervous and can only see the soldier if front of him. If that soldier is facing him, he assumes that he is wrong and reacts in exactly one second by turning around. After two seconds, the soldiers look like this:
In another second, they react in the same way. The sergeant rolls his eyes and decides to wait for them to settle down before giving another order. How long will it take before he can tell them to face forward again? Is this a worst case? What initial reactions take the longest for them to settle down? What about if there were n soldiers, n a positive integer, instead of 6?
Project Idea(s)
Prerequisite Mathematics: Familiarity with some of the ideas of discrete math would probably come in handy.
Required Programming Level: Elementary.
Key Words: automata, combinatorics
Reviewer: K. M. Levasseur (Kenneth_Levasseur@uml.edu)
Archive: none
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