At the end of Twisting on the Magic Paving Stones,
I noted that there was something unexpected.
Please look back over previous articles to see the full details but, in
short, what I was discussing is a scenario in which, in each round of a sort of
game, a number of magic paving stones (≥2)
are inserted at random locations (with an evenly distributed likelihood) into a
path, then a monster takes a step from one paving stone to the adjacent one
closer to you (starting at one step closer to you than the last paving stone in
the path) and then you eliminate one paving stone of your choice (and since you
don’t want the monster to get you, you are going to eliminate one behind it,
further away from you).
Set the number of randomly inserted paving stones to 2, the initial
pathlength to a sufficiently large value (for which I choose 120, so the
monster starts on paving stone number 119) and plot the output once every 200 rounds
and you get this:
It might not be immediately
obvious, but we’ve seen something like this before (or at least those of us who
looked at the OE curve). To emphasise
this, here is that monster location curve with the OE curve below it – noting that
smoothing has been turned off.
This is rather curious and was in fact something that I was struggling
with – having previously posted two articles on the same sort of thing before retracting
them (soon to be reinstated at Observable
Events Curve - Is Double Dipping Essential? and Observable
Events Curve - Not Quite a Drunkard's Walk).
Note that the time (or number of rounds) that is taken for the monster to get you (or “capture time”) is not set, there’s something akin to chaos happening in that the capture time very much depends on slightly different conditions early in the scenario, which – after the first round – are randomly imposed.
