Can water solve a maze? [video]

He&#x27;s wrong about why that maze towards the end of the video doesn&#x27;t empty out the supply tank. It&#x27;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.<p>This is why you don&#x27;t have water pipes in your house go up and down loads of times. It can cause an air lock preventing water from flowing.

Reminded me:<p><a href="https:&#x2F;&#x2F;en.m.wikipedia.org&#x2F;wiki&#x2F;Water_integrator" rel="nofollow">https:&#x2F;&#x2F;en.m.wikipedia.org&#x2F;wiki&#x2F;Water_integrator</a><p><pre><code> 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. </code></pre> Also see &quot;A brief history of liquid computers&quot;: <a href="https:&#x2F;&#x2F;royalsocietypublishing.org&#x2F;doi&#x2F;10.1098&#x2F;rstb.2018.0372" rel="nofollow">https:&#x2F;&#x2F;royalsocietypublishing.org&#x2F;doi&#x2F;10.1098&#x2F;rstb.2018.037...</a>

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).<p>Also makes me wonder what a proof would look like.

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.<p>The static solution can be calculated by solving the Poisson equation. In [1] you can see a small implementation of the idea.<p>[1] <a href="https:&#x2F;&#x2F;simulationcorner.net&#x2F;maze&#x2F;" rel="nofollow">https:&#x2F;&#x2F;simulationcorner.net&#x2F;maze&#x2F;</a>

Very nice.<p>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 &quot;on the lip&quot; (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.<p>I do agree though that it&#x27;s a rather unexpected behavior.<p>[1] <a href="https:&#x2F;&#x2F;www.youtube.com&#x2F;watch?v=81ebWToAnvA&amp;t=370">https:&#x2F;&#x2F;www.youtube.com&#x2F;watch?v=81ebWToAnvA&amp;t=370</a>

So it&#x27;s basically A* with higher scores when going towards gravity, very cool.<p>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)&#x2F;v_walking = (sin β)&#x2F;v_swimming and the fastest path is the one which just happens to satisfy this angle constraint

&gt; [2:39] ... Actually a maze becomes very easy to solve if you colour the two parts separately.<p>Breezing through that example like he didn&#x27;t just blow my mind, wow. It makes so much intuitive sense.

This reminds me of this classic paper [1] &quot;Maze Solving by Chemotactic Droplets&quot;. Oil droplets sense a chemical gradient as variation of interfacial tension, using what is commonly known as the &quot;Tears of wine&quot;, or Marangoni effect, to propel themselves to the exit.<p>[1] <a href="https:&#x2F;&#x2F;pubs.acs.org&#x2F;doi&#x2F;full&#x2F;10.1021&#x2F;ja9076793" rel="nofollow">https:&#x2F;&#x2F;pubs.acs.org&#x2F;doi&#x2F;full&#x2F;10.1021&#x2F;ja9076793</a>

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.

For sufficiently large mazes it must get harder to push the water through. Water can&#x27;t solve a Tesla valve. (<a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Tesla_valve" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Tesla_valve</a>)

I&#x27;ve often wondered, is this vaguely analogous to the quantum wave function and what&#x27;s happening when particles try all possible paths?

Maze solving by gravity assisted literal flood-fill [1]<p><a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Flood_fill" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Flood_fill</a>

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 <a href="https:&#x2F;&#x2F;www.thingiverse.com&#x2F;thing:5948252" rel="nofollow">https:&#x2F;&#x2F;www.thingiverse.com&#x2F;thing:5948252</a> <a href="https:&#x2F;&#x2F;www.youtube.com&#x2F;watch?v=S748mcM0MSg">https:&#x2F;&#x2F;www.youtube.com&#x2F;watch?v=S748mcM0MSg</a><p>As Steve showed, it&#x27;s particularly important to take into account both air and water.<p>There is still some work needed to make it Sim2Real and optimize the design automatically.<p>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&#x27;s a story for another day).<p>Quite fun, messy and time-consuming rabbit-hole to go down to, cause you need to get the details right.

This reminds me of The Dumbest Way To Solve A Maze [1] by Numberphile - similar approach. Posted on HN before [2]<p>[1] <a href="https:&#x2F;&#x2F;www.youtube.com&#x2F;watch?v=BvwgdrC8vlE">https:&#x2F;&#x2F;www.youtube.com&#x2F;watch?v=BvwgdrC8vlE</a><p>[2] <a href="https:&#x2F;&#x2F;news.ycombinator.com&#x2F;item?id=32799511" rel="nofollow">https:&#x2F;&#x2F;news.ycombinator.com&#x2F;item?id=32799511</a>

The practical application of this fluid maze is the automatic transmission&#x27;s valve body:<p><a href="https:&#x2F;&#x2F;youtube.com&#x2F;v&#x2F;u4kM67f_P3A?t=23">https:&#x2F;&#x2F;youtube.com&#x2F;v&#x2F;u4kM67f_P3A?t=23</a><p>Tangent: Change your transmission fluid. Lifetime transmission fluid spec is the lifetime of your vehicle&#x27;s powertrain warranty.

Now do it with a superfluid [1].<p>[1] <a href="https:&#x2F;&#x2F;en.m.wikipedia.org&#x2F;wiki&#x2F;Superfluidity" rel="nofollow">https:&#x2F;&#x2F;en.m.wikipedia.org&#x2F;wiki&#x2F;Superfluidity</a>

You can also solve a maze with Cellular Automata: <a href="https:&#x2F;&#x2F;github.com&#x2F;philtomson&#x2F;CellularAutomata#you-can-solve-mazes-with-a-cellular-automaton">https:&#x2F;&#x2F;github.com&#x2F;philtomson&#x2F;CellularAutomata#you-can-solve...</a>

Also have a look at this interactive simulation: <a href="https:&#x2F;&#x2F;app.physion.net&#x2F;scenes&#x2F;water-maze-solver" rel="nofollow">https:&#x2F;&#x2F;app.physion.net&#x2F;scenes&#x2F;water-maze-solver</a>

Would this work as well if the maze had horizontal path instead vertical, when gravity and bottom-up air pressure wouldn&#x27;t be helping the water find the path? I think it would look more like the one from Bergman Joe.

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?

Simple video, yet fascinating

What happens if we use a Tesla valve for a maze?

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

A computer is a computer, and our universe is a computer. So, it&#x27;s possible we&#x27;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.