Can water solve a maze?

This video explains why I had a blue splodge on my face in the last video!
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You know what I think can solve the puzzle flowing through the main path right away?? Smoke! Pushing smoke into the puzzle, it will flow through the path of least resistance from the start

the fact that a maze is two separate pieces blew my mind more than the water maze. It makes perfect sense but I have never thought of that!

Directly to the experiments in less than 1 minute, now this is the channel that deserves to be popular.

Someone should make a free demo and share or code for a 3d simulation, this could be in unity or unreal or something like that.

The "keep your right hand on a wall" always works, IF you start doing so from the entrance!
A maze may have two or more paths to the exit and therefore has more than two wall structures, but it will always have just two outside ones.

5:28 Even in a multiply-connected maze (one with multiple successful paths), you can be sure that the walls of the ENTRYWAY will be the walls of the exit, as long as the entry and exit are on the outside border of the maze. I didn't realize that until you showed your "coloring the walls" at 2:50 then mentioned that two paths would create a middle part. That middle part won't be the left or right wall of the entrance, but would necessarily be an "island" in the middle. The interesting thing is that you can't just wander around and decide later to use this algorithm: you need to commit to it at the very entrance to the maze. And, it only works if the exit is also on an external wall, not say a stairs in the middle of the level, or say a goal or treasure of some kind not adjacent to an exterior wall.

Regarding surface tension, try solving the smaller maze with 'wetter' water. Reduce the surface tension of water by dissolving some alcohol in it. :) Might be interesting with different fluids as well.

Definitely one of these concepts that I never would've thought about on my own but are really interesting if someone brings them up.
If you wouldn't mind the mess, you could maybe drill small holes near the top of the "air chambers", so the water could push the air out of the maze and get closer to bergman's simulation?

I really think you should look into getting the big versions of the mazes into a gallery. They are really beautiful art pieces against that white background. The blue liquid is really radiant

Hi, great video, I love the mazes! I have a different hypothesis for why the water doesn't fully drain from the reservoir though (5:50), I believe it is likely that the maze is essentially creating numerous "P" traps that causes air bubbles between the different sections. After all the P traps are full, new water would have to compress the air in the bubbles to make room for the new incoming water, causing the resistance. Though if you added enough water pressure to push the air bubbles all the way through I bet you would get some proper syphon action!

This is fascinating, really nice work on constructing the mazes too.

You could try substituting the water with some type sort of oil used in vacuum pumps to test the maze under a vacuum. The oil shouldn't be too hard to get your hands on and they all have very low vapour pressures

Realizing every maze has two halves was a surprising revelation I didn’t expect.

Every now and then I find videos like these that are on more of the complicated side of things and they really intrigue me. It just scratches the right spot on my brain to keep watching

Regarding the 2 paths leasing to 3 walls you can 'hug'. It still works holding the hand on a wall, if you do so when you enter the maze. The 3rd middle part that loops wont be one of the walls at the entrance. So unless walls are shifting its a pretty safe approach

As a physicist, I must say that it looks oddly satisfying (and accurate). This is the first time I see this channel btw. Immediate subscription activated 😌

Possibly beyond the abilities of your laser cutter, but if you could make a membrane with holes which were small enough to let through air but not water you might be able to recreate the BergmanJoe maze that way. Lots of "air escape hatches"

This is actually very similar to how valve bodies work in automatic transmissions. Great stuff!

I had never thought of a maze being in two halves - and yet it's so obvious when you think about it! Steve is like the Johnny Ball of the digital age 🙂

This is amazing. You could hypothetically have a huge containment of water with multiple maze plugs of different tensions to simulate different distributions instead of larger or smaller ducts

I had a feeling it would be surface tension being too strong for the water to overcome it. You present your paradoxes and caviats in such a good manner its more like an assist than me just knowing it

The water in the tank came to a halt like a car going uphill with its engine’s torque just short of power. The water in the maze needed more weight pushing down so it could push up all those nooks and crannies and fight against gravity and surface tension alike. Truly fascinating. :)

6:00 not only just surface tension but as you said earlier for the small mazes, air pressure. The first lip looks impossible if no air prevents the water from moving. All the little pockets of air that you see have formed along the correct path (unlike the incorrect path in the small model, although there is still some of that) to help hold up that massive head of water.

I cant believe how many things I learned from this. I was not expecting this much from a "pouring water in maze" video! 😃

what a cool way to do science! i have to say that ive never thought about weather water could solve a maze but i was not expecting the results you came up with. a-maze-ing!

I have wondered about this for a long time. Wondered but never quite sure if I could build it. Thank you for building and showing it.
For the surface tension try adding soap.

This shows the difference between physical and digital simulations. In digital there is always something overlooked like the ire pressure in this situation which is why its always important to test the digital one on a small scale first.

That last part is so interesting. Blue water has figured out the maze and now the red water can go directly to the end with virtually no loss

As someone who's explored a lot of computer game maps I will say the idea of putting your left hand on the wall and trying to just follow it almost always works but you can end up with geometries where it has you always avoiding the turn that you need to take so if you do that approach can you find yourself circling back to where you started switch to the other wall.

It's funny watching this as a software engineer because a lot of these different algorithms are used in machine learning. For instance the large simple maze takes the path that "takes you lower" and is actually a searching algorithm called depth first search used to find an end goal state.

very interesting, I'm glad I got here. I have a question: regardless of the erratic movement, there seems to be a pattern, however what would happen if the entrance/exit of the maze was at the left/right sides?

I like your videos, because of the way you present things. It's like the way I do things in my head. I love puzzles and mazes. Have you tried using a 3d printer to make the things

There are couple of important things this experiment shows, especially when dye is added. It shows what happens when there are unused lines in water delivery piping (like for example building hydrants sharing same line with tap water). It can become breeding ground for bacterias, eg. Legionella, despite water moving, and that's why it's important to use backflow prevention valves.

Great job Steve... I see all your videos.... And you explain a complex concept in easy way..... ❤️❤️

I love how straightforward the video was. Thank you for getting right to the point and not wandering around.

Getting stuck in a three part maze with my hand on the wrong side without knowing it is a new fear you just unlocked in me. Thanks for that lol.

This is pretty awesome, I now want to build something similar to mount on the wall in my shop/office as a water feature.

You are an amazing scientist and a top-class educator.

I loved the solution of cutting slots in the upper acrylic plate to allow the solvent to reach the surfaces you wanted to solvent weld.

If you "print"/etch a maze pattern on a circuit board and apply electrodes to the exit points and run electricity through it and look at it with a FLIR infrared scope you should see a solution too with the right settings. :-) (provided the the travel path is where the metal film remains and the walls are actually voids where the metal has been removed :-) ) The set up should have no trouble solving gigantic complex mazes, as big as the circuit board can be and with small channels down to the printing resolution. 🙂

At 2:38 how about creating grooves that match with the maze and flooding the grooves with solvent? Hope it helps in future videos. Thank you for the video Steve!

Oh wow, I hadn't thought of a maze being constructed of two pieces but that makes sense now that I've seen it and given what I remember about graphs. My mind went to bipartite graphs and partitions first, since there are no odd cycles. But then I realized I was overthinking it, there are no cycles at all, it's just a tree in this type of maze. Of course you can partition a tree into two disjoint sets. :)

Thats so cool to see and a bit hypnotic I could marvel at water flowing for a long time having one of those mazes in a case with colored water cycling through it sounds like a fitting decoration for a high end office I want one it reminds me of my water timer for board games way more fun to use

This would be a good physics game type of thing. I could watch this for hours, literal hours.

Regarding using the "hand on one wall" method to go through a multipath maze, as long as you pick a wall right at the entrance then you should still always find your way out. Any extra paths would create a third piece to the maze, but by necessity it would have to be in between the two outer parts which must be the two parts bisected by the entrance and exit.

Hi,
Good points about the role of atmospheric pressure and surface tension. It should not be very difficult to take this into account in simulations as well.

Videos of the build process would be awsome. Coming up with a question is easy, coming up with an experiment that answers it, is part art, part science.

It would be interesting to see pressure gauges in certain areas

You could make a liquid calculator for integrals. Might be interesting :)

Your tests are great to be used by cave divers, people going deep underground exploring cave systems.
So that in case of storms outside and flooding in the caves, they ca use as a model to predict safe places for setting up camps.
I've seen a story about such a situation of a deep dive and a storm that lasted several days outside leading to huge flooding in the cave.

If you wanted to simulate the simulation you could put a small vent hole at the top of each isolated section of the geometry and then just cover/plug the hole once water starts leaking out of the venting hole. That should be easily done in the larger versions and you just need something like flex tape to cover the vents. it won't look as pretty but the physics should work.

I think in order to make Joe's simulation, you could use fill the entire system with a fluid, then use another fluid with similar density that will not mix. Sort of like water and oil, but not quite, since oil is less dense than water. (i dont know of any more hydrophobic fluids haha)

I think the realization that every maze is essentially two parts and the shortest-route-to-exit is always the point where the two halves meet is - itself - a solution were you ever actually inside a maze. All you'd need is some way to tell which wall was attached to one side of the maze and which wall is attached to the other side. Perhaps if the walls were conductive and were insulated by the ground/ceiling you could run a wire between each to know when you closed the circuit so know you've gone the wrong way.

I would have liked to see the maze in a horizontal position too because I think it would allow the air in those dead end areas to escape so maybe the water would have gone to more areas before exiting

Would love to see this inside a vacuum to see if it's closer to the simulated model

I think a circular maze with the exit or treasure (because it's not technically an opening) in the center would be a more interesting challenge as there is no exit for air anymore and water should behave differently in this case.

With your second complicated, big maze, I don't think it is surface tension but an air lock, the path repeatedly goes up then down so if there is a bubble in each up bit, it requires a minimum head of water to overcome the sum of the uphill parts.

What if the Bergman simulation is a bird's eye perspective of a maze with an open top that just being flooded?

This seems like a clearer example on why there are sometimes air pockets in caves and other such areas. Interesting

Suggestion: try and put the maze flat on its side, so that the air from the air pockets will escape into the exit. This should greatly reduce air pressure, and therefore make the maze work as intended. Have a good amount of water going in as well.

Suggestion: AMBITIOUS idea with real life application... the air pockets remind me of the Tham Luang cave rescue, where 13 boys survived a monsoon in a cave system by finding the room with air. I never understood how there was enough air underground until this video. Could there be a way to 3d map cave systems and simulate flooding to find the safest places to survive in such events?

man, you really nailed the lighting on the larger mazes, the contrast of the "walls" is perfect

It’s an air lock, there’s too many areas where- as you said before- have air bubbles that have to travel downward before they can go back up to make way for the water. This takes the momentum and flow of the initial pour and weight of water in the reservoir- at a certain point the momentum and weight of the water gets low enough, that the residual air pockets and pressure neutralize it and it stops flowing.

The two colors of water made me think it could be cool to see that but where the whole maze is completely filled with the first color. If you use a slightly more dense second liquid (salt water?) maybe that might simulate the animation through mixing?

I think the sim would probably be best recreated if it was possible to fill the maze completely with water first, then fill the top tank with colored water and finally open the exit of the maze, although the flow would probably not be as energetic as in the simulation, having water in its way already. 🤔

2:14 I like how water can’t solve the harder maze but the air bubbles can

Funny thing about solving mazes with water, it can be easily done also horizontally (you placed the maze vertically and let the water flow from top to bottom). Think maze walls as hills, and corridors as the valleys in between, let the water rain into the maze.... and boom, water will flow out following the perfect solution path. This can be implemented easily on computer progam using the watershed algorithm.

I love by the way how you included the animation clip at the beginning but still motivated us to watch the original which supports its creator. Just love it

Lots of cool observations, well done!

It really fits my ocd to see water or any liquid go through any maze I love the video great keep the content up

Hey Steve
Just a thought. What would happen if you put the maze horizontally and “shot” water through the maze? Would the water solve the puzzle differently then?

Have you thought of building a neural network with water? Pipe diameter can represent the connection weight and the activation function can be an overflow mechanism.

An effective way of applying the acrylic solvent to the maze and the second clear sheet would be a very fine layer in a level metal pan. Holding the already applied acrylic side, dip the maze portion into the pan. Immediately lift it up and apply a slide rotational swirl to remove any gathered droplets. Then move the it, still maze down onto the s wall already placed on the ground. A simple corner frame can be built-in utilize to make a quick into make sure it is square. It has to be removed from the thin layer of solvent and place on the other surface quickly without any torque. Light pressure, then give it a few. Largely depending on the solvent use to melt the acrylic, this is a very effective method.

I actually used this once in a dnd campaign. Our DM put us in a huge mirror maze room. Using a combination of a few magic items, I made a torrential downpour of water and we waited a minute before following the flow

It’s not surface tension that’s causing the maze to stop working, it’s vapor lock. The same thing can happen in piping systems when air gets trapped at high points. The air blocks part of the pipe and reduces the area that the liquid has to flow through. This constriction causes head loss and eventually the combined head loss across multiple constrictions becomes so severe that it equals the head pushing the fluid. This means that there isn’t enough pressure to move the fluid and the flow stops.

Regarding the effect of air pockets and surface tension. I think it is possible to minimize the effect of this, by angling the maze forward or backwards. This will reduce the height difference and allow the air pockets to pass the liquid by not utilizing the full channel width and or hight.

I think the key is that you have enough pressure from above to force the water to move against gravity. If you only had enough to navigate the maze and a bit more, it might not force the water all the way through

I did enjoy this video. Very much. You are clearly now a 80000 hours expert on building acrylic models !

Love this! Mazes were "my thing" at school. We had exercise books with squared paper in them for maths, and I used to draw mazes all the time, so I became really familiar with a lot of stuff about them. The "stick to one wall" rule is a good window into some of them, as it makes you think about where the entrance and exit might be (could be in the middle), whether it still works with multiple entrances, whether there's a way to use it to escape a maze if you start in a random spot (there are algorithms that can eliminate dead ends as you go, but they require some sort of memory or external modification)...
A third dimension also stirs things up. The maze at Longleat in England (which was the largest in Europe in the 1980s, not sure whether it still is) has six bridges that go over the hedge paths. This allows you to see some of the connectivity from above, which people imagine might help - but the presence of the bridges also makes the topology more sneaky and the maze harder.
I LOVE MAZES! Cool to see your construction skills applied to them like this. Excellent video.

What a cool video, thank you for making this!

To this point, a maze that starts at the outside and ends in the center of the maze would only be found if the end was "surface-tension-lower" than the beginning, or maybe you could spin the maze like how you fill up a Klein bottle or something...

It looks to me you are trying to solve SAT problem :) and this approach is actually realy interesting !

Drilling small holes in each 'top' corner to allow air to escape may allow you to recreate the behaviour in the simulation more closely, though would need to be quite small to provide sufficient resistance to water flow

its a good tool for showing aquifer water behavior it also replicates a concealed aquifer with the tank being a river stream or lake pretty cool

This video actually made me realize that if you just try to visualize how the maze is in two pieces it becomes easier to solve visually. Pretty cool! I also think it works how a siphon works.

you should try to do it with the maze almost horizontally like 5° with no top cover and higher walls... Just close the "entrance" so it became a container and should behave more like the simulation since you're removing the "air gap" variable.

I'm curious what would happen if you drilled a hole in the back side of the air pockets to allow the air a path out. This might make a closer representation to the simulation.
Second, could you try this on a horizontal maze as well?

I would love to see this done with smoke also, possible explain other aspects even more

If you want to do this maze without the air but with liquid you could use two liquids with different densities. Like Oil and water. You have to fill the maze completely with oil and then fill water in. The water should flow to the lowest point.
... i think
Cheers :D

at 6:02 you talk about surface tension as a cause for the maze to remain stuck. I think you are not counting the loss of pressure due waterfalls. For example at 6:15 you draw an arrow over "staircase" section, it should be noted that across that section the water does not increase is pressure (assuming the air has neglicible mass). So everytime that water is in free fall it gets to a lower point without increasing in pressure. I count about 27 such drops in the entire path with is about the same height of the water level relative to the exit of the maze

5:40
True,
if you only start using the 'hand on wall'-tactic as a backup plan, after you've already been in the maze for a while a multi-solution one can trap you.
Doing so from the start will work (for any 2 dimensional maze, where 'out the other side' is the goal. Get to the centerpiece artwork (or staircase to the exit-tunnel), are made out of 1 piece and may loop you back to the entrance )

beautiful to watch! much more than the simulated version

It all follows a very logical process, the only thing I had not accounted for personally was the combined surface tension to be enough to halt the flow. I simply predicted a full empty beside the deeper areas or a stop of flow relatively quickly if no air could enter from above.

6:15 I think it's also that you have vertical paths with no water now, those are parts with no down pressure push water up the other side.

About the "never get lost in a maze"-thing: It does work all the time, because you choose to go right or left, but you take that choice at the beginning and never stray from it. So there's no way for you to chose to go around the middle part forever, if any actually exists, because you chose one of the other parts at the beginning. The simplest form of that kind of maze would be a room with a pillar in the middle, an entry, and an exit. As you enter, you choose the wall to your right, or the wall to your left, the pillar is completely out of the question.

Thank you for the video. I will try to create a small labyrinth on a 3d printer with a transparent petg.
Perhaps I will try to make a version that will allow air to pass from one of the walls using a 10 micron fabric membrane.

You've scaled up one of the dimensions of the system without scaling any of the other relevant variables (viscocity, density, simulation time). Neat to see how the system changes from that one input.
I'd be interested to see this run by scaling all of the relevant variables to keep the system's relevant dimensionless numbers the same (reynolds number, etc). Would make for a great fluid dynamics example. Smarter every day or veritasium did a video on a boat research that talks about this a little
EDIT: It's veritasium's video at a naval wave generator

Would using a gas denser than air work more like the video or would it be fairly similar to the water?

The fact that you always has 2 pieces for a working maze means that the topology is a real science.