Is this how the Escher Waterfall machine works?

Yesterday, I blogged about an anonymous YouTuber who appeared to have built a machine that could make Escher's impossible self-replenishing waterfall a concrete reality. David Goldman thinks he knows how it was done, and sent this diagram along.

(Thanks, David!)

I write books. My latest is a YA science fiction novel called Homeland (it's the sequel to Little Brother). More books: Rapture of the Nerds (a novel, with Charlie Stross); With a Little Help (short stories); and The Great Big Beautiful Tomorrow (novella and nonfic). I speak all over the place and I tweet and tumble, too.

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Anonymous

Only the water is CGI. The model is real. If you watch when he is pouring the water into the box just below the wheel, you can see the flow doesn’t match how much is being poured. Then, as the water travels around the right angles, it flows all even and smooth. It would he the right angle hard and you would get a lot of splashing. It’s not bad, but it reminds me of CGI from the 90s where as opposed to the modern day stuff.

Now go back to dreaming about unicorns.
Sheekus

beautiful I always love how Escher expands our mind’s of what’s both possible and contradictory. It’s like seeing both flatland and 3d at same time.

speaking of mind expansion by cognition:
I wrote recently a post that’s on a similar theme, titled “how to have eternity in an hour”
http://www.cybernoeticman.com/2011/02/how-to-have-eternity-in-hour-in-5-easy.html
Anonymous

Oh, and the waterwheel is on a motor so it starts spinning at his control.
Anonymous

Like my 9 year old daughter said the other day:

“It’s amazing that no one has ever done anything impossible!”
irksome

I STILL say “God dunnit”.
Anonymous

The diagram that David Goldman presents looks quite different from what we see in the original video; I overcolored it , see at
http://mennucc1.debian.net/escher_not_solved.jpg :
I colored red some pieces that do not appear in the original, and green a piece that is instead missing (and is not the only one). So in my opinion David Goldman really got it wrong.
Anonymous

I call this design tinyurl.com/65d24qw since shadows and reflexes are coherent, then he poured water on each level and composited all together. He spoils it by showing us the two big buckets full of coloured water: why so much if he has a perpetual waterfall that to function needs just the waterï»¿ in the blue jug? He needed to pour lots of water on each level to obtain a constant and long enough flow that looked convincing once composited. Nice, well done!!!
EeyoreX

Um, the pillar supporting (A) doesn’t appear that way at all in the video. In fact that pillar is part of the optical illusion and probably doesn’t even exist as such.

So this may be the correct scematics for how this trick is created, but it doesn’t work out any of the details, like balance or support or perspective or such.

(B) is just redundant btw. Somebody go get Occhams shaving tools.
Lucienz

Hey, great post on the most possible solution!
I did have to comment on the “itâ€™s probably CG because that would be easy” side of things.
Creating an accurate fluid dynamic animation that looks real, with all the imperfections in reality, is actually very difficult.
Also, if the creator of this is good enough to make something of that quality there is no reason for the camera to be locked down. If he had the model, lighting, texturing, and shadow motions in 3D he could have done a handheld video moving around the thing without too much more effort that would have added to the realism.
In short, not 3D. All speaks to the solution given: Two shots masked and comped in a 2D operation in post (bunch of reasons why the â€œpumpâ€ solution probably wouldnâ€™t work as well)

Second, I don’t think anyone mentioned this but you can see that the “leading” edge is higher than the rest of the trough and it all flows downhill. If you look at the pour point you can see that the bottom of the trough is not on the ground. The further along the track you follow the thinner the whole device gets. Itâ€™s a uniform trough and side walls made at an angle to fool the eye.

Look at the explanation 3D model, imagine it tilted down then watch the video again. You can see it.

Anyways, amazing practical trick shot on the video and great work again on the solution!
Anonymous

Just look at the video in 1080p. You can clearly see the splitline where the two video takes are joined. Look at the “roof” of the tallest tower – the one above the waterfall’s edge.

Yes, there seem to be artifacts of post-processing, faking some shadows etc, but this is a wood model and the water flow was shot in two takes, one for the left side of the model with a bucket on the right, and the other way round.
Anonymous

Or it is CGI…the wood is just too brightly lit. And considering it looks to be unprotected pine, it would have instantly have started soaking up the water and darkening.

Everything in that shot is dirty, dark and wet…except the waterfall which seems to have the most amazing and perfect lighting. And nothing else reflects in the water on the floor quite as nicely. Wierd…to get it this lit, I would expect to see lights in the water too.

It would be awesome if this were anything more than CGI…and it would be possible to make an illusion that looked like this…but it ain’t it. Actually, part of the fun of these sorts of things is to see how someone did it…and unfortunately, this is too easy.
- Anonymous
  
  @Anon#1. No I don’t think it’s CGI.. where’s the cleverness in that? It would just be too damn easy to do this as CGI in post-production these days. No, this is a clever piece of forced perspective, enough to even fool some into thinking it is just CGI.
millrick

damn you, Boing Boing, for destroying my delusions
– i LIKE to believe in impossibile things
subhan

@#1 – the scene is very brightly lit because I believe it to be clever forced perspective filming. It requires a very small aperture to get large depth of field, and thus needs very brightly lit scenes. For a masterpiece of this kind of work watch Darby O’Gill & The Little People. They nearly cooked the actors to death during the filming of some of the scenes with the intense lighting used.
Anonymous

Here is my explanation– a combination of CGI, illusion, and trickery:

1. The woodwork is real in the sense that he did construct something that from the right angle only LOOKS like the Escher’s waterfall. However, I don’t believe the waters runs through it in real life. This is where the CGI comes in.

2. When he pours the water, the water escapes through an exit right after the trough (hidden by the water wheel).

3. The illusion part of the video, which is water going uphill to the waterfall is done in CGI, and it’s very easy to do so. Simulating water flow upwards with CGI in straight lines is CGI 101.

4. And lastly the water dropping from the fall onto the wheel is real. This is the trick part. I believe he has a tube going up to the fall portion (obstructed inside or behind the inside column), and he probably triggers this with his free hand since he’s mostly outside of the camera view. It could also be started by someone else in the room, that part is irrelevant.

Anyhow, that’s my theory and if you can agree that Escher’s waterfall can be built to appear as such from a specific point of view (without running it, just as a still image), the rest I assure you is possible. Points 2-4 are 100% feasible.
Anonymous

you can see the unit is above the ground it is suspended or lifted
AdrenalineSleep

I’d like to see someone use THIS model to do the same trick to see if the result in fact replicates the video.

I tried to study the movements in the video and kept pausing as he walked past the thing thinking that the shadows would help reveal the illusion but i just couldn’t get my head around it. This is awesome.
Anonymous

If that is an electrolyte solution he is pouring in there, it could complete a circuit to turn the pump on at just the right time.
That would be more elegant than leaving the pump running anyway.
dmatos

That pretty much matches up with my opinion of where the break in the real model is. However, I don’t think the video was necessarily done in two cuts. If there is a reservoir and a pump underneath the floor-level track, it would be fairly trivial to hide a tube running from that reservoir up to point A on the above diagram. Water falling off the end of point C could be collected by the reservoir.

The tricky part would be timing starting the pump, so that the C->A transition is as tidy as possible. He did a great job, but there is some inconsistency in the water flow at ~0:45 in the video.
bodenski

When thinking about HOW one would easiest make this illusion, I thought it COULD be as depicted here, OR COULD have the slices marked A and E attached to C and the water pipe hidden behind the upright and come out at the corner.
I think the video looks great!
Cunning

oops? Hardly. Mcwolles’ waterfall is truly epic and nearly flawless. The fact that he didn’t sweat a few environmental giveaways bespeaks a certain humility if you ask me. It’s all about the project, not the presentation.
gavintree

I am sort of upset with david and all the rest of you. Listen, he is obviously making the water flow uphill. I watched the video and the water clearly is poured in at the bottom and runs up to the water fall and then cascades back down to the bottom. The paranoia being exhibited on this thread is terrifying.
pjk

nice, two thumbs up. the guy who made this had to have known that the most fun part of these things is figuring out how he did it. thanks for the treasure hunt!
asbuuu

I agree the most likely way he did it was by cutting the water flow behind one of the pillars. It doesn’t have to be ‘C’ as suggested. I don’t see any noticeable time delay there.

Also, you can see the water appear in segment ‘B’ for a brief second, and the reflection of the water is always apparent, so I do think it’s attached to the main track.

It is mind boggling how well he did this (if he did). Remember, in order to get forced perspective looking right, lines we assume are parallel have to be cut at very precise, non-parallel angles. To work with wood in this way would be extremely difficult. So either he’s a master wood cutter and illusionist, or perhaps this whole thing was done with rather simple tricks in ‘post-production.’ I just don’t know.
Anonymous

Well this diagram is a little off IMHO. The trough “appears” to enter the left tower BETWEEN the middle and right pillars, not from behind. I think that the discontinuity in the water is hidden behind the middle pillar of the left tower, not the left pillar of the right tower. Rather than a small triangle for the middle level of the left tower, the entire near edge of BOTH sections of trough where the water is flowing from right to left are attached to the left tower, as evidenced when his shadow passes over the near edges without darkening the surfaces of the trough. (There must be a smaller near edge hidden from view by the false near edge attached to the left tower) And, like dmatos, I don’t think that there is a break in the film. however it does look like there is more water spilling over the water wheel than is making it to the end of the trough.

And just to say it, talking how this was done DOESN’T demean it, rather it is a teastamant to how engaging this little video is.
stalkingcat

I really don’t think there’s a break anywhere in the video.

When he pours the blue water out of the reservoir bucket, the water starts swishing around, and stays consistently swishing throughout the entire video. If you just stare at the bucket, there’s no apparent break.

David’s diagram? Looks correct, but there’s some kind of pump back at C.
Anonymous

This proposed solution is too clever by half. I don’t think its all that complicated, with pumps and editing and such. The only split in the design that needs to be carefully done is around the waterwheel which appears to be in the foreground, but to work hydrodynamically for this illusion, is probably ‘really’ at the end of the trough, away from viewer. The trick is to make it appear with foreshortening gimmickery to be ‘in front’. No pumps, editing, CGI. The simplest explanation is usually correct, nice trick!
scopeyPDX

If he were going to cut the video, it would have made it much easier if he’d moved entirely out of the frame. There’s got to be a pump somewhere, so no reason not to have a circular system.
Anonymous

Reminds me of http://blog.makezine.com/archive/2009/08/james-dysons-uphill-water-flow-illu.html#
Anonymous

Looks really good.

I would only like to add that I think that the shape of the “machine” in my opinion must have acute edges and C is connected with A+E. If you look at the motion of water in 0.46 you can see a swirl, a u-turn, of water. Besides declining base of the water tunnel, starting at D, I think that entire ground of the room is sloping up. Hence, the level of water at C is roughly same as at D, which would explain the lag. Also, the inclining floor allows space for the bridge.

I took the liberty of editing the original diagram to show what I mean about the bridge.
http://img573.imageshack.us/i/solved.jpg/
- EeyoreX
  
  “I think that entire ground of the room is sloping up… Also, the inclining floor allows space for the bridge
  
  So, in effect, what youÂ´re saying is that the water actually flows upwards and creates an infinite loop, that this machine bends the laws of physics and that weÂ´re back at square one.
  And you even took the time to alter the drawing to illustrate this point?
  
  I’m afraid there’s no polite way to say this: You, sir, are an idiot.
cosmorphis

Does it have to be solved? Can’t it just be cool?
Anonymous

I would have thought that the water hitting the wheel would create a splash of some kind, which would deflect into the surrounding puddles on the concrete, mimicing some sort of mild rain effect…

…cant see any ripples though?
Anonymous

Wrong. That doesn’t match up with his model at all.
Anonymous

The water does run into B when there is a wave at around 1:04. But I agree with you on the rest of it.
Anonymous

I agree with EeyoreX… the pillar in the design doesn’t match the video
Anonymous

I have already commented on the YouTube video and will make my points here as well
This structure never exited in optical illusion form. It is obviously a CG manufacture. Two very clear reason:
Reflection does not match image. If the water reaches the base of the structure there should not be a black line.
http://i54.tinypic.com/29o5ts2.jpg

the perspective angles are wrong in the reflection. given the reflection in the water, the horizon would be in the room.
http://i56.tinypic.com/29nvtbk.jpg

Not to mention if you zoom in at 1080p you can see pixelization from manually editing the frames. This can be seen on the pillar on the bottom inside corner (fourth from left), along its left edge. Also at the top of the pillar, third from the left. When you zoom in you can see where they slipped with their brush, the color protrudes into the trough sidewall.
- Anonymous
  
  @Anon you wrote “Reflection does not match image. If the water reaches the base of the structure there should not be a black line.
  http://i54.tinypic.com/29o5ts2.jpg”
  That’s true unless the structure is not touching the floor. The start of the ramp might be lifted to make the water flow faster.
Anonymous

Bravo to the trickster who invented this!!!
Seriously, man, this is really cool work.
I hope you won’t let these nit pickers discourage you from future work. What you’ve done is incredible optical angular science.
Thanks so much for showing us how you did it. Really sweet.
Few people would have had the courage to “fess up” and show us.
I hope you will do more and I hope Hollywood finds a full scale use for this. They almost did in the Inception movie. You never know, it might make you some moolah. Best wishes!!!
Pavelo77

Hello, here’s my explanation :)

http://flic.kr/p/9jKyHA

I think that David’s solution doesn’t hold up, the shadows wouldn’t match.
Anonymous

Um…. hey guys?
Look at the shadows of the setup. You can clearly see how the towers are spaced and seem to be exactly what the explanation is drawn as
Anonymous

I think there is certainly a break at C / A & E, but I’m not convinced there’s a break at B.

Here’s a screenshot with some notes that points out evidence of the break: http://i.imgur.com/Kqgtr.jpg
Anonymous

Here’s what I see.
http://i39.photobucket.com/albums/e165/mdhockey7/waterfall.png

The parts I put in red are just extensions to look like the retaining walls. They help hide the ends of pillars that don’t support anything, allowing them to be cut without a precise angle because the tips of them are hidden behind these extensions.

I’d guess there is a pump hidden inside the base under the wheel. The base would act as an extra reservoir to hold water that was preloaded for the pump.
voiceinthedistance

Useless diagram without a notation for where the magnets are located.
Anonymous

all the shadows are painted on, not CGI.
VJ

@ANON#9: You are right that the model above could not be correct because the trough appears to go through the pillars at B and not behind them as this model above would produce. Because the trough runs through the two pillars twice each, I think this is most likely computer generated. If it were a physical object, the left pillar would either have to be closer to us than the right pillar or farther away (even if it the trough was not continuous). The left pillar cannot be both closer than the right one and farther away at the same time. That is also the illusion used in the original Escher drawing.