Imagine a Maze of Twisty Little Pathways.

A project log for Computer Motivator

If you don't know what a computer motivator is by now, then you have been reading too many textbooks and not watching enough TV.

glgormanglgorman 09/13/2021 at 16:040 Comments

In Reno Nevada, if you know exactly where to look (stay tuned for a hint), you can find this lovely labyrinth.  Which of course would be an ideal maze for a small robot to solve.  Even though the terrain might be a little bit rough for a small robot like a Boe-bot, but imagine the possibilities.

This is a kind of an epiphany of sorts.  Since a very long time ago, I implemented my own open OpenGL Stack, or a least a subset of OpenGL entirely from scratch, and one of the things that I thereupon decided to experiment with was doing things like calculating "Cauchy's Integral Formula", for those who are familiar with the theory of complex variables.  Getting at least some hooks into some OpenGL routines appears to be very doable on the Parallax P2 chip, with its built in HDMI, VGA and standard NTSC/PAL or whatever capabilities., and of course there is the Propeller Debug Protocol, so that if a robot could be built that builds a kind of "OpenGL" like world view, while it does the job of exploring its environment.  Ah, the possibilities!

Shades of West-World?  "How do I find the center of the maze?"  "What if the maize isn't for you?"  What if "they" are supposed to be the ones who "think differently".  Oddly enough, imagine a game where there is a hidden treasure behind the front door on the right, but there also might be a bomb, or some hungry trolls that have an appetite for human flesh, eagerly awaiting to pick the flesh from the bones of any mere mortal who tries to take this game too seriously.   Ouch.  The only way to disarm the bomb, or be prepared for the trolls, is to find the center of the maze.  This is easy for a simple spiral, but probably nonetheless quite difficult for an AI, even in simulation.  

Interestingly enough, if you understand "Cauchy's Integral Formula" from calculus then you know that it is possible to compute an integral, i.e., the integral of dz/(z-z0) along some path in the complex plane, and that the result should be 2*pi*"square-root-of-minus-one" times the number of times that (z-z0) takes on the value zero INSIDE the path.  Which means that one can calculate whether a given point is either INSIDE or OUTSIDE an arbitrary enclosed region!  And yes, it does work for a really big, weird spiral, that is to say - if you have the map.

O.K.., I admit that this is a HARD problem.  Probably very hard even for a Tesla Robot.