Escher's "Relativity" in LEGO®

Because The LEGO Company get paranoid about this sort of thing let me make it clear that I have no affiliation with them, that my views are my own and do not necessarily represent theirs, and so on. So if you think any of this is official you are as deluded as they are.

Click on the picture or here for a bigger version (about 410K)


Daniel Shiu and I worked on this as a joint project after we finished our rendition of Escher's "Ascending and Descending", making it our fourth Escher picture rendered in LEGO. Once again, no camera tricks, but the picture has to be taken from exactly the right place, and boy did we get tired of trying to find where that place was. The whole thing took five or six evenings spread over two or three weeks. Most of the last evening was taken up with setting up the lighting the way we wanted it and trying to get the camera position just right...

The original Escher picture (Relativity, 1953. Lithograph) is shown on the right for comparison.

Unlike many of Escher's other "impossible" pictures (like "Ascending and Descending") , there is actually no optical illusion involved here. Gravity seems to be working in three different directions simultaneously, but the picture shows a perfectly self-consistent physical scene. So modelling it should certainly be feasible. But while Escher's picture has three different "up"s, LEGO isn't quite so flexible...

For LEGO afficionados, the most significant thing about our version is the widespread use of SNOT ("Studs not on top") techniques - in plain English, having the LEGO studs pointing in lots of different directions. There are various tricks for making this work in general, and we probably used all of them here. You can find some of the details in the construction pictures.


Some Construction Details...

Click on the small pictures for larger versions.


Here's the final construction, taken from a slightly different angle and further away so you can see what's going on. It's all a bit messy - lots of scaffolding to hold it all up.

The early stages of construction

A SNOT detail: This little man sitting on his bench was constructed as a separate module....

...that fixes under here. The technique here is to use Technic 1/2 pins sticking into 1x1 Technic beams. The head of the pin protrudes sideways (= upwards in this picture) and can be used as a LEGO stud to plug into the bottom of a brick. The bench itself is a 1x4 brick with studs on the side.

The same 1/2-pins-and-beams trick was used to fix this vertical railing to the wall. Here I've pulled it off so that you can see what's going on. Of course the really tricky thing here is getting the spacing right because of the 6/5 height-to-width ratio of a LEGO brick, but 4 studs width = 3 bricks and a plate high. So it's not entirely accidental that the railing supports are 4 studs apart from each other...

This staircase and arch was fixed to the wall in the same way. Here I've pulled it away from the wall and turned it round. Of course the stair/arch construction itself is pretty SNOTty. I'm not entirely happy with the way we did this, but it was the best we could manage. We used 1x1 headlight bricks to fix the arches to the stairways.

Here I've pulled off the tower and bridge which appear on the right of the finished picture. The direction of the studs changes at the end of the stairs. The technique here is to use a Technic pin to hold together two 1x1 Technic beams oriented at right angles to each other, and join everything else to the Technic beams.

Finally, here's another overall view. This time you can see some of the lights we used for the final photograph. Yes, I know it's not very professional-looking. As a final (though invisible in the finished picture) ea=xample of SNOT, notice the vertical green baseplate behind the far wall. This is there to stop the light on the right shining through the doorway at the top of the model. It is fixed on with yet another technique: A couple of 1x4 bricks are fixed on the baseplate, and their studs fit into the holes in a long Technic beam which clips onto the top of the wall.









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