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Can water solve a maze? [video]

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Re: Can water solve a maze? [video]

#51

Post by xmcqdpt2 »

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.

Re: Can water solve a maze? [video]

#52

Post by patates »

pxeger1 wrote: post #38
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.

You can make a maze with only one path (other than paths that double back on themselves), but has three pieces: https://i.imgur.io/R4j6TH3_d.png I think this is basically a flaw in the intuitive definition (or maybe only my intuitive definition) of "doubling back".

That maze has 3 solutions though. If there is only one solution, without reversing, it has to be 2 pieces.

Re: Can water solve a maze? [video]

#53

Post by patates »

bilsbie wrote: post #49

Not sure if mazes are np complete but if so could we map other problems into maze designs and the water can solve problems for us?

If you extend the definition of the maze a bit, aren't all circuits mazes?

But then, you can keep extending it and say that everything is a computer and also a maze.

Anyway, the brain gymnastics is a lot of fun, at least for me.

Re: Can water solve a maze? [video]

#54

Post by xmcqdpt2 »

pxeger1 wrote: post #38
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.

You can make a maze with only one path (other than paths that double back on themselves), but has three pieces: https://i.imgur.io/R4j6TH3_d.png I think this is basically a flaw in the intuitive definition (or maybe only my intuitive definition) of "doubling back".

In your case there are technically two paths through the maze (straight through and going through the loop).

Re: Can water solve a maze? [video]

#55

Post by xmcqdpt2 »

bilsbie wrote: post #49

Not sure if mazes are np complete but if so could we map other problems into maze designs and the water can solve problems for us?

They are not NP at all. A perfect maze (with one solution) as a connectivity graph is a tree. Finding the path through a tree can be done by DFS in linear O(N) time.

Re: Can water solve a maze? [video]

#56

Post by programmer_dude »

docandrew wrote: post #44
quickthrower2 wrote: post #27

Earlier quoted context omitted.

Even without consciousness, the existence of the universe faces the same causality issues.

All the talk of simulations, multiverses, etc is IMO expending a lot of effort to avoid facing the possibility of a Creator - the “uncaused cause” or something existing outside of time and space.

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

Re: Can water solve a maze? [video]

#57

Post by jagged-chisel »

GistNoesis wrote: post #45

Inspired by Steve mould, I had some fun doing something quite similar a while ago experimenting with Bell Siphon, 3d printing, and numerical simulation. If this interest someone here I just pushed it to Thingiverse now https://www.thingiverse.com/thing:5948252 https://www.youtube.com/watch?v=S748mcM0MSg As Steve showed, it's particularly important to take into account both air and water. There is still some work need…

> 404 you’ve reached the end of the thingiverse

Re: Can water solve a maze? [video]

#58

Post by beanjuice »

This reminds me of this classic paper [1] "Maze Solving by Chemotactic Droplets". Oil droplets sense a chemical gradient as variation of interfacial tension, using what is commonly known as the "Tears of wine", or Marangoni effect, to propel themselves to the exit.

[1] https://pubs.acs.org/doi/full/10.1021/ja9076793

Re: Can water solve a maze? [video]

#59

Post by GistNoesis »

jagged-chisel wrote: post #57
GistNoesis wrote: post #45

Inspired by Steve mould, I had some fun doing something quite similar a while ago experimenting with Bell Siphon, 3d printing, and numerical simulation. If this interest someone here I just pushed it to Thingiverse now https://www.thingiverse.com/thing:5948252 https://www.youtube.com/watch?v=S748mcM0MSg As Steve showed, it's particularly important to take into account both air and water. There is still some work need…

> 404 you’ve reached the end of the thingiverse

Sorry republished it, should be OK now

Re: Can water solve a maze? [video]

#60

Post by pwagland »

pxeger1 wrote: post #38
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.

You can make a maze with only one path (other than paths that double back on themselves), but has three pieces: https://i.imgur.io/R4j6TH3_d.png I think this is basically a flaw in the intuitive definition (or maybe only my intuitive definition) of "doubling back".

Except that this maze clearly has at least two solutions. Straight through the corridor, or via the loop. And that's assuming you don't wander around the loops n times.
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