12 ms·
Can water solve a maze? [video]
- Qubus 4y agoAlso have a look at this interactive simulation: https://app.physion.net/scenes/water-maze-solver https://app.physion.net/scenes/water-maze-solver
- Darky 4y agoSimple video, yet fascinating
- OscarCunningham 4y agoFor sufficiently large mazes it must get harder to push the water through. Water can't solve a Tesla valve. (https://en.wikipedia.org/wiki/Tesla_valve https://en.wikipedia.org/wiki/Tesla_valve)
- deleted 4y ago[deleted]
- bell-cot 4y agoYes, water can solve a Tesla valve: > Steady flow experiments, including with the original design, however, show smaller ratios of the two resistances* in the range of 2 to 4.[6] It has also been shown that the device works better with pulsatile flows.[6] *Ratio of resistance to water flowing "forward" vs. "backward" through the Tesla valve. Though if you stretch things far enough - say, a thick layer of "waterproof" clay - your statement is correct for most purposes.
- hinkley 4y agoRectifying diodes also have limitations for how much reverse voltage they can block. When I fiddled with circuitry I was surprised how low that could be for cheap rectifiers. It sank some of my naive designs. Real circuits can have transistors or resettable fuses to handle out-of-spec situations and shut down.
- s-macke 4y agoIf 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/ https://simulationcorner.net/maze/
- willis936 4y agoSome if Buls Berglund's recent videos about waves in mazes made me realize this. Funnily enough he uploaded a video two hours ago that shows what it looks like. https://youtu.be/lBLlYmM6tjU https://youtu.be/lBLlYmM6tjU
- xmcqdpt2 4y agoAFAIK 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.
- simondotau 4y agoIt 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.
- fooker 4y agoIt would have been even more interesting if this was not in the linked video!
- simondotau 4y agoSorry, I didn't explain myself well enough. I mean start with the maze completely filled with water such that there's no pockets of air left, and water pressure is sufficient for water to race through continuously. Then introducing a distinct dye. The difference would be that it would have far less turbulence from splashing/pooling.
- tromp 4y agoMaze solving by gravity assisted literal flood-fill [1] https://en.wikipedia.org/wiki/Flood_fill https://en.wikipedia.org/wiki/Flood_fill
- jjbinx007 4y agoI've often wondered, is this vaguely analogous to the quantum wave function and what's happening when particles try all possible paths?
- _Nat_ 4y agoRelated links: https://en.wikipedia.org/wiki/Pilot_wave_theory https://en.wikipedia.org/wiki/Pilot_wave_theory https://en.wikipedia.org/wiki/De_Broglie%E2%80%93Bohm_theory https://en.wikipedia.org/wiki/De_Broglie%E2%80%93Bohm_theory https://en.wikipedia.org/wiki/Hydrodynamic_quantum_analogs https://en.wikipedia.org/wiki/Hydrodynamic_quantum_analogs
- jjbinx007 4y agoThank you
- grupthink 4y agoA computer is a computer, and our universe is a computer. So, it's possible we're living in a simulation but not one that was intentionally constructed by a higher life form, but rather, a simulation that emerged from nature (e.g. electrons whizzing along the surface of silica rock on a desolate planet). Our universe could recursively be computers all the way down.
- NayamAmarshe 4y agoA computer is always imperfect though, compared to the universe, which is very stable and extremely perfect to the last detail. I don't think we can even compare since the scale and the domain is so vast.
- codetrotter 4y agoIf a tree is standing in a forest, but no one is there to watch it. Does the tree get rendered every frame?
- archerx 4y agoYes, it does.
- ndsipa_pomu 4y agoNo, it doesn't.
- NayamAmarshe 4y agoDepends on the programmer.
- yazaddaruvala 4y agoDepends on the hardware being targeted.
- polishdude20 4y ago
- freetime2 4y agoThe 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.
- Enginerrrd 4y ago>Also makes me wonder what a proof would look like. I think you need to be very careful in how you define a maze, lest you run the risk of rediscovering the difficulties involved with the Jordan Curve Theorem.
- ndsipa_pomu 4y ago> Also makes me wonder what a proof would look like. Start with the simplest possible maze (i.e. one square with a start and a finish) which will be in two pieces. Then show that all possible additions will not add further pieces except for when you "cut" into an existing piece to make a separate non-solution route (i.e. a looped route that takes you back to the same point). (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")
- dmurray 4y ago> (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.
- ndsipa_pomu 4y agoOr 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.
- DavidPiper 4y ago> [2:39] ... Actually a maze becomes very easy to solve if you colour the two parts separately. Breezing through that example like he didn't just blow my mind, wow. It makes so much intuitive sense.
- lupire 4y agoUnless you are the maze constructor, coloring the maze pieces is at least as hard as solving it.
- hinkley 4y agoIf you color it the way he describes solving the maze (by keeping one hand on the wall the whole time), then solving it and coloring it should be the same operation, yes? Because if you haven't touched part of that wall yet, then you aren't at the exit. And anything you haven't touched is part of a different piece.
- JumpCrisscross 4y agoNow do it with a superfluid [1]. [1] https://en.m.wikipedia.org/wiki/Superfluidity https://en.m.wikipedia.org/wiki/Superfluidity
- mnw21cam 4y agoHe'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. This is why you don't have water pipes in your house go up and down loads of times. It can cause an air lock preventing water from flowing.
- quickthrower2 4y agoI thought so, because the first area of surface tension he pointed out is disconnected from the rest of the water. So that surface tension alone would have to explain it. But there was a lot of water up there! I guess it is the same as the upsidedown glass of water with a sheet of paper underneath trick.
- Retric 4y agoMostly, 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 roughly an inch but it’s worth testing.
- mywacaday 4y agoWhat'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?
- 123pie123 4y agowater has a fair number interesting properties https://www.chemistryworld.com/features/the-weirdness-of-water/4011260.article https://www.chemistryworld.com/features/the-weirdness-of-wat...
- _v7gu 4y agoSo it's basically A* with higher scores when going towards gravity, very cool. Another physics problem analogue I really like is the problem of fastest travel from point A to point B when you have to cross a river. One approach to solve is is to treat it as a minimization problem by writing down everything, another one is to realize light beams have already solved this problem for you, and the problem becomes much simpler when your river entry angle α and swimming angle β have to satisfy (sin α)/v_walking = (sin β)/v_swimming and the fastest path is the one which just happens to satisfy this angle constraint
- PartiallyTyped 4y agoAssuming the heuristic follows triangle inequality, then it is A*.
- lazyant 4y agoanimals like ants and dogs intuitively "solve" the equation too
- huhtenberg 4y agoVery 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 behavior. [1] https://www.youtube.com/watch?v=81ebWToAnvA&t=370 https://www.youtube.com/watch?v=81ebWToAnvA&t=370
- rrobukef 4y agoIt 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.
- deleted 4y ago[deleted]
- GistNoesis 4y agoInspired 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.thingiverse.com/thing:5948252 https://www.youtube.com/watch?v=S748mcM0MSg 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 needed to make it Sim2Real and optimize the design automatically. The ambitious end-goal, is to have a cascading siphon (not so dissimilar than the flushing mechanism in your toilet) that can reliably be switched on by a single additional drop of water. (Currently I achieve this goal using a Shishi Odoshi fountain to arm the siphon very reliably but it still has one moving part, but that's a story for another day). Quite fun, messy and time-consuming rabbit-hole to go down to, cause you need to get the details right.
- jagged-chisel 4y ago> 404 you’ve reached the end of the thingiverse
- GistNoesis 4y agoSorry republished it, should be OK now
- bilsbie 4y agoNot 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?
- thih9 4y agoI thought we decided to use electricity and silicon mazes instead? But there were attempts to use water too, e.g. MONIAC: https://en.m.wikipedia.org/wiki/MONIAC https://en.m.wikipedia.org/wiki/MONIAC
- patates 4y agoIf 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.
- xmcqdpt2 4y agoThey 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.
- brokensegue 4y agoall P problems are in NP \pedantic
- beanjuice 4y agoThis 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 https://pubs.acs.org/doi/full/10.1021/ja9076793
- andreygrehov 4y agoThis reminds me of The Dumbest Way To Solve A Maze [1] by Numberphile - similar approach. Posted on HN before [2] [1] https://www.youtube.com/watch?v=BvwgdrC8vlE https://www.youtube.com/watch?v=BvwgdrC8vlE [2] https://news.ycombinator.com/item?id=32799511 https://news.ycombinator.com/item?id=32799511
- deleted 4y ago[deleted]
- 1970-01-01 4y agoThe practical application of this fluid maze is the automatic transmission's valve body: https://youtube.com/v/u4kM67f_P3A?t=23 https://youtube.com/v/u4kM67f_P3A?t=23 Tangent: Change your transmission fluid. Lifetime transmission fluid spec is the lifetime of your vehicle's powertrain warranty.
- dukeofdoom 4y agocan this work with light? how would it be different. just trying to imagine a light solving a maze
- CyberDildonics 4y agoLight 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?
- noobcoder 4y agoYou 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.
- agilob 4y agoSounds like more known name for it is "ant colony optimisation". Lots of computer science algorithms and structures are based on that principle https://en.wikipedia.org/wiki/Ant_colony_optimization_algorithms https://en.wikipedia.org/wiki/Ant_colony_optimization_algori...
- agilob 4y agoWould this work as well if the maze had horizontal path instead vertical, when gravity and bottom-up air pressure wouldn't be helping the water find the path? I think it would look more like the one from Bergman Joe.
- scarmig 4y agoReminded me: https://en.m.wikipedia.org/wiki/Water_integrator https://en.m.wikipedia.org/wiki/Water_integrator The Water Integrator (Russian: Гидравлический интегратор Gidravlicheskiy integrator) was an early analog computer built in the Soviet Union in 1936 by Vladimir Sergeevich Lukyanov. It functioned by careful manipulation of water through a room full of interconnected pipes and pumps. The water level in various chambers (with precision to fractions of a millimeter) represented stored numbers, and the rate of flow between them represented mathematical operations. This machine was capable of solving inhomogeneous differential equations. Also see "A brief history of liquid computers": https://royalsocietypublishing.org/doi/10.1098/rstb.2018.0372 https://royalsocietypublishing.org/doi/10.1098/rstb.2018.037...
- miketery 4y agoWhen I first started learning EE I conceptualized it with water. Ie voltage / potential is a higher water level vs else where. But this takes it to a whole new level, impressive!
- albrewer 4y agoWhat's funny is the math is identical between resistor - inductor - capacitor circuits, spring - mass - damper mechanical systems, and tank - pipe - valve fluid systems. The main difference between them is how you calculate the equivalent of resistance, inductance, and capacitance.
- marcosdumay 4y agoIf you search the web (or only Youtube), there are even digital water computers out there.
- pradn 4y agoThere's a whole Wikipedia page for the water-electricity analogy: https://en.wikipedia.org/wiki/Hydraulic_analogy https://en.wikipedia.org/wiki/Hydraulic_analogy
- deleted 4y ago[deleted]
- UncleOxidant 4y agoYou can also solve a maze with Cellular Automata: https://github.com/philtomson/CellularAutomata#you-can-solve-mazes-with-a-cellular-automaton https://github.com/philtomson/CellularAutomata#you-can-solve...
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- LonelyWolfe 4y agoWhat happens if we use a Tesla valve for a maze?