Here's the scrambler, a carnival ride out of my childhood:
I'm curious where my red cart will be when the ride finishes. To begin with, you might tell me a location where my red cart definitely won't end up. Ordinarily I'd ask you what information would be helpful for you to help me answer my question, but in the interest of time, I think this may help you here:
My sense is there are a number of different ways to answer my question but I'm not sure how many. Please post your thoughts in the comments and as precise a location of the red cart as possible. I'll update this in two days with the answer.
BTW. A follow-up question (or "sequel" in the three-act parlance): if you trace a path behind the red cart as it moves, what will the path eventually look like? (This is called a "locus" but I suppose it's best if we postpone formal vocabulary development until our debrief.)
2013 Feb 01. Here's the video as it runs down to the end of the ride:
And here's a killer Desmos calculator that lets you adjust all kinds of parameters on the scrambler.
Great work in the comments. Several people analyzed the periodic nature of the scrambler. Others