Introduction

What is a Hash?

    A Hash is a running event that simulates a British fox or rabbit hunt.  Typically runners follow a trail of arrows, X's and F's, laid out ahead of time, with the goal of reaching a party at the end.  The catch, however, is that the trail will break about every quarter mile and branch off into several false trails and one true.  The false trails are relatively short and terminate at F's.  The true tails lead to the next break point.  X's, called "checks," signify the breaking points, but also signify that one is on the right trail.  For added  complexity, the runners usually have to search for the continuing trail, true or false, after encountering an X.  The event begins at an X.

    Additionally, there is an aspect of communication in a hash.  When running the trail, hashers will call out "ON ON" when they encounter an arrow, "FALSE" when they find a trail to be false, and "CHECK" when they find an X.  Ideally, runners can hear the calls of their distant companions and correct their own course accordingly.

    For details on Hashing and the Glories there of, visit A Treatise on the Hash.
 

Our simulation

    We are generating a computer simulation of the hash to observe the statistical properties of the event.  Our goals for this simulation include mimicking as close as possible the behavior of a real hash, using the rules listed below, and finding a relation between the complexity of the "hash field" (the hash course) and the time necessary for all the runners to finish.  The trick of this simulation will be to integrate the influences of environment (the X's and arrow's) and communication between the runners.

    Our applet shows a field of cells we call a hash field.  Within this hash field are X's and F's as discussed above, but instead of arrows it uses a number system where 4 is left, 8 is up, 6 is right, and 2 is down, as is on your number keyboard.  The runners start out at the central X, each moving with a random walk until they recognize a trail marker.  If they find an arrow they will no longer move randomly, but follow it's direction.  If the runners find an F, they retrace their steps.

    In running the applet, clicking your mouse on the hash field screen will advance the simulation by one time step.

Runner Attributes - Constant in time.

    Endurance - Each runner can only move a certain number of spaces before
                        taking a rest.  That number of spaces and the length of time spent
                        resting are chosen randomly for the runners.  This definition of
                        endurance effectively dictates a speed for each runner.

    Gullibility - How likely is a runner going to follow another runner.  For our
                        simulation gullibility is measured on a 0 through 9 scale, 9 being
                        completely gullible.

Communication

    Whenever a runner encounters a trail marker, it lets other runners around it know.  In life, when runners encounters an arrow, they calls out "ON ON," to let everyone know where there is a trail, be it true or false.  The effect of an arrow being found is that other runners within hearing range will decide whether to follow there own paths or turn toward the arrow just found.

    When runners encounter an F, they call out "False" to let everyone know that the trail is false.  The effect of an F being found is that other runners on that same false trail will turn back when they hear the trail is false, that trail now being avoided by those not on the trail.

    And when runners encounter an X, they call out "Check" to let all the other runners know where the true trail is.  The effect of a check being found is that all the runners will immediately turn to converge on that point.

    As with real Hashes, the runners in our simulation communicate by calling out "ON ON," "False," and "Check," and are always listening for answers to the following questions:

    Have arrows been found by anybody?

    Has the trail been found false?

    Have checks been found by anybody?

 
When they receive news about an arrow being found, runners have an xx% chance of following the call instead of following their own path, as determined by their gullibility.  When runners receive news about false trails or checks, they act as stated above.