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Can water solve a maze? [video]

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Re: Can water solve a maze? [video]

#81

Post by krisoft »

ndsipa_pomu wrote: post #79
krisoft wrote: post #77

Earlier quoted context omitted.

Meh. Sophistry. Changing definitions to get unexpected results is boring. The simple truth is that the original proposition "all mazes being two pieces" is just false. Obviously false when you have multiple exists, or when there is only one exit/entrance and the goal is to reach the middle of the maze. But even if we stick to one entrance one exit mazes you can have multiple paths from exit to entrance which cut the…

>But even if we constrain ourselves to one entrance, one exit mazes with a single solution path you can trivially construct a maze inside a large room without connecting it to the walls. Thus creating a third piece to the maze. I would be intrigued to see that "trivial" solution - how do you prevent there being two routes (and thus solutions) around the third piece without connecting it to the wall?

I see what you are saying, yes the maze wouldn't have only a single solution after the construction of an inner maze.

Re: Can water solve a maze? [video]

#82

Post by btbuildem »

freetime2 wrote: post #15

The thing that I found most interesting was actually the little side discussion about all mazes being two pieces. Something that I had never considered, but seems fairly self evident (assuming only one path exists through the maze). Also makes me wonder what a proof would look like.

> all mazes being two pieces

This is true for mazes with only one path from start to end. Each additional path necessitates a separate piece (path permutations nonwithstanding)

Re: Can water solve a maze? [video]

#83

Post by ndsipa_pomu »

krisoft wrote: post #77
ndsipa_pomu wrote: post #64

Earlier quoted context omitted.

Or define that the "maze" is the collection of all the reachable areas from the start position. Then, it doesn't matter what you do in inaccessible areas as they're not part of the maze.

Meh. Sophistry. Changing definitions to get unexpected results is boring. The simple truth is that the original proposition "all mazes being two pieces" is just false. Obviously false when you have multiple exists, or when there is only one exit/entrance and the goal is to reach the middle of the maze. But even if we stick to one entrance one exit mazes you can have multiple paths from exit to entrance which cut the…

I'd consider it to be specifying the "maze" more accurately. The idea is to be able to come up with an interesting statement (such as "all mazes of this type can be made of just two pieces"), but if you include non-reachable areas as part of the maze, then it reduces the number of interesting statements available but also doesn't add to the process of examining the routes and solution.

If you consider the same type of maze but have it in three dimensions, then all of them can be made out of just one piece, so it's clear that the definition of "maze" is too encompassing.

Re: Can water solve a maze? [video]

#84

Post by jeanlucas »

btbuildem wrote: post #82
freetime2 wrote: post #15

The thing that I found most interesting was actually the little side discussion about all mazes being two pieces. Something that I had never considered, but seems fairly self evident (assuming only one path exists through the maze). Also makes me wonder what a proof would look like.

> all mazes being two pieces This is true for mazes with only one path from start to end. Each additional path necessitates a separate piece (path permutations nonwithstanding)

He says that in the video...

Re: Can water solve a maze? [video]

#85

Post by noobcoder »

You should check how bacterias navigate through mazes. They can navigate through complex environments (chemotaxis and swarming). Bacteria can sense gradients of chemicals and adjust their movements accordingly to find the optimal path through a maze. The ability of bacteria to communicate and coordinate their movements to solve more complex mazes is hella impressive.

Re: Can water solve a maze? [video]

#86

Post by CyberDildonics »

dukeofdoom wrote: post #74

can this work with light? how would it be different. just trying to imagine a light solving a maze

Light goes in a straight line an reflects. If the walls are diffuse, a tiny amount of light is always going to make it out at some point, but what does that have to do with this?

Re: Can water solve a maze? [video]

#87

Post by Moissanite »

btbuildem wrote: post #82
freetime2 wrote: post #15

The thing that I found most interesting was actually the little side discussion about all mazes being two pieces. Something that I had never considered, but seems fairly self evident (assuming only one path exists through the maze). Also makes me wonder what a proof would look like.

> all mazes being two pieces This is true for mazes with only one path from start to end. Each additional path necessitates a separate piece (path permutations nonwithstanding)

> mazes with only one path from start to end

One of my favourite bits of trivia: it is this property (being "unicursal") which leads to a maze being more specifically characterized as a labyrinth.

Re: Can water solve a maze? [video]

#88

Post by programmer_dude »

NayamAmarshe wrote: post #67
programmer_dude wrote: post #56

Earlier quoted context omitted.

The presence of a creator does not change anything. Who created the creator?

The creator remains without a creation. The notion that most schools of thought have is, the creator is unborn and born at the same time and has always existed. Creator does not have a point of creation, not even death because those rules only apply to the materialistic universe.

That's quite a cop out. Excuse me if I don't take your word for it.

Re: Can water solve a maze? [video]

#89

Post by CrazyStat »

mnw21cam wrote: post #73
btbuildem wrote: post #66

Earlier quoted context omitted.

How does that reconcile with the syphon principle? You'd figure that once the water is flowing out of the end, even if the tank was below some of the water's path, the flow would continue until all the water was gone.

Siphons work best once air has been excluded from the path. In fact, they work exactly as the opposite to why this maze isn't draining the whole source tank. In a working siphon, the head of water in the downwards direction is greater than the head of water in the upwards direction, which pulls the water forwards. In this case, because of the air columns in the down direction, there is a greater head of water in the…

Yep. It's easy to test for yourself that a siphon will quickly stop working if you let too much air into it.

This is also why you can't make very tall siphons, as if the pressure gets too low at the top the water will boil off, create a gas pocket of water vapor, and stop the siphon.

Re: Can water solve a maze? [video]

#90

Post by delecti »

albert_e wrote: post #78
freetime2 wrote: post #15

The thing that I found most interesting was actually the little side discussion about all mazes being two pieces. Something that I had never considered, but seems fairly self evident (assuming only one path exists through the maze). Also makes me wonder what a proof would look like.

Hmm interesting indeed. He also shows that you can use the "bucket fill" paint tool on any part of the maze to automatically highlight and visually "separate" that half from the other half of the maze. Now can we use THIS property to automatically solve a maze? make the WALLS of the MAZE themselves out of transparent TUBES and fill THEM with dyed water? An then the solved maze is simply the path that always has dyed…

Most maze solving algorithms don't really interact with the maze in that way. You generally act on cells/spaces and whether or not the adjacent cells are connected or blocked.

To use this property on a maze you'd have to traverse the whole maze using the typical cell adjacency, reconstruct it in a format that lets you bucket fill the walls, do that, and then also construct an algorithm which acts using the different colored walls. It only really works for a person interacting with a maze in a format where they can bring it into a picture editor.

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