[FRIAM] solving mazes

[Alexander Rasmus]

Nick,

Assuming that every intersection is 3-way isn't enough to guarantee that
the maze is simply connected, see attached. If you put the exit in the no
go region then the wall following strategy doesn't work, as entrance and
exit won't be connected.
[image: maze.png]

Best,
Alex

On Sat, Feb 27, 2021 at 5:10 PM cody dooderson <d00d3rs0n at gmail.com> wrote:

> I am assuming this is a 2D maze. Wikipedia does a better job at explaining
> the problems with wall following than I can.
>
> *If the maze is not simply-connected (i.e. if the start or endpoints are
> in the center of the structure surrounded by passage loops, or the pathways
> cross over and under each other and such parts of the solution path are
> surrounded by passage loops), this method will not reach the goal.*
>
>
>
>
> On Sat, Feb 27, 2021, 1:48 PM <thompnickson2 at gmail.com> wrote:
>
>> Hi, All,
>>
>>
>>
>> Due to a review I have been working on, I have been dragged back into
>> thinking about maze learning in rats.  Any animal I have ever known, when
>> confined, will explore the boundaries of its enclosure.  Cows, for instance
>> will beat a path just inside the barbed wire that encloses them.  So a maze
>> is not only a series of pathways but it is also an enclosure.  If the rat
>> puts his left whisker against the left wall of the maze, he will eventually
>> get to the goal box, right.  It works with the Hampton Court Maze.  On the
>> second run, he can now use odor cues, such that any time he encounters his
>> own odor both entering and leaving a passage way, he should just skip that
>> passage way.
>>
>>
>>
>> So I am wondering, you topologists (??) out there, how general is the
>> statement, “every maze is an enclosure”  and what is the limitation on the
>> idea that any maze can be solved by putting your right or left hand on a
>> wall and continuing to walk until you find the goal or are let out of the
>> maze.  Now I should quickly say that rat mazes are usually composed of a
>> series of bifurcating choice points, where the rat can go either left or
>> right. Some choices lead ultimately to dead ends.  In sum, a runway in such
>> a maze can go straight, turn R or L without choice or form a T with a right
>> or left choice.  My intuition is that no such maze can be designed that
>> does not permit the boundary following strategy.
>>
>>
>>
>> Nick
>>
>>
>>
>> Nick Thompson
>>
>> ThompNickSon2 at gmail.com
>>
>> https://wordpress.clarku.edu/nthompson/
>>
>>
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