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Can water solve a maze? [video]

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Re: Can water solve a maze? [video]

#71

Post by simondotau »

xmcqdpt2 wrote: post #51
s-macke wrote: post #4

If you are using a gas rather than a liquid, it is even simpler. Just set a high pressure at the beginning and a low pressure at the end. The gas will automatically follow the steepest part of the pressure gradient. The static solution can be calculated by solving the Poisson equation. In [1] you can see a small implementation of the idea. [1] https://simulationcorner.net/maze/

AFAIK this would also work with an incompressible fluid like water if you started the maze fully filled than add a sink at the exit and a source at the entrance. You wouldn't have any bubbles in that case and the current would flow along the solution.

It would be interesting to see what would happen to a fully filled maze if, once you got a steady continuous flow at the entrance and exit, you injected some dye into the water at the maze entrance.

Re: Can water solve a maze? [video]

#73

Post by mnw21cam »

btbuildem wrote: post #66
mnw21cam wrote: post #20

He's wrong about why that maze towards the end of the video doesn't empty out the supply tank. It's not surface tension, but rather it is the fact that the path goes up and down. The down parts of the path will be filled with air, and the up parts will be filled with water. Water is more dense than air, so the supply must have more pressure than the sum of all the heights of the up parts in order for water to flow. T…

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 upwards direction than the downwards direction, causing a reverse back-pressure.

Re: Can water solve a maze? [video]

#75

Post by krisoft »

mywacaday wrote: post #47
Retric wrote: post #42

Earlier quoted context omitted.

Mostly, but surface tension in aggregate is meaningful. Surface tension is doing two things, first it’s contributing to back pressure several times in the same way it’s just barely keeping water from over topping. Secondly it’s taking up volume in air pockets thus increasing the pressure of those pockets. So, if he added soap to reduce surface tension the tank wouldn’t empty but it would end up lower. My guess is rou…

What's great about this video and the discussion is that something as familiar as water can have new and non intuitive things to learn about it. Are there any other examples of common things that have non obvious behaviour from every day experience?

> Are there any other examples of common things that have non obvious behaviour from every day experience?

How about the chain fountain (also from Steve Mould): https://www.youtube.com/watch?v=_dQJBBklpQQ

Re: Can water solve a maze? [video]

#77

Post by krisoft »

ndsipa_pomu wrote: post #64
dmurray wrote: post #61

Earlier quoted context omitted.

> (Having any loops in the maze would break the condition of there being only one solution as you could take a detour round the loop as many times as you like and thus have an infinite number of "solutions") The loop could be somewhere inaccessible from the starting point. Perhaps your logic holds if you insist that all pathways in the maze are connected, though.

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 maze into multiple pieces.

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.

It is just simply false.

Re: Can water solve a maze? [video]

#78

Post by albert_e »

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 walls on one side and transparent walls on the other. Not sure what the mathematical proof for this will look like but sounds nearly as good as the original "water can solve a maze" proof?

Re: Can water solve a maze? [video]

#79

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…

>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?

Re: Can water solve a maze? [video]

#80

Post by [deleted] »

rrobukef wrote: post #40
huhtenberg wrote: post #37

Very nice. I think that the explanation given for why the water stops flowing [1] is wrong. It has likely less to do with the surface tension "on the lip" (see video) and more with the fact that that all air bubbles in the maze become pressurized and their cumulative pressure is enough to push back on the water trying to get into the maze and prevent it from flowing in. I do agree though that it's a rather unexpected…

It shouldn't be, because every bit of upwards pressure towards the exit is compensated by the same amount of downwards pressure on the path before. I'm surprised there is that much static resistance in the maze.

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