"Hyperbolic tiling": can you escape from an extradimensional prison?

Originally published at: http://boingboing.net/2017/02/13/hyperbolic-tiling-can-you.html


“Now tell me, what, I, say
Hyperbolicsyllabicsesquedalymistic” -Isaac Hayes

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There is a fifth dimension beyond that which is known to man.
It is a dimension as vast as space and as timeless as infinity.
It is the middle ground between light and shadow,
between science and superstition,
and it lies between the pit of man’s fears and the summit of his knowledge.
This is the dimension of imagination.
It is an area which we call… the Alt-Fact Zone.



Before I play the game, you should be able to move forward and backwards (or left/right, up/down) at the same time, and in fact that should be a method to the solution, if there is one.

You just move back in time until a point where the prison wasn’t yet built.

In answer to the thread title, yes.


took me about a minute

You can’t move in 4 physical dimensions but s’purty though.


If you get close enough to that wall it seems like it might be possible to use the procedural generation of the vertexes to re-tile geometry around the camera if you move along a hyperbolic vector whilst also turning in proximity to one of the encroaching edge-planes.

I’ve got it to go only so far (in hyperbolic wall generation) before the geometry starts to disappear but I feel like if I could get the back/forward aspect of the procedural generation algorithm, or at least the activation thereof, I could re-tile the prison around myself from outside it.


If one were to create a pocket universe to house a fractal prison, i think the way to get around the “moving through time” to escape would be to loop time so that the prison exists in all points along the timeline.

Go through the triangles?
worked fer me.

So that’s not the Windows 11 desktop? Good, I guess.


Thanks. I just lost the game. :expressionless:

Moving away from the prison, the thing starts to jiggle around by itself. A floating point rounding error?



A couple of days into this thread and we’ll have it singing and dancing for us!

Movement works by applying 4x4 matrices that implement hyperbolic isometries. These have exponential functions in them, and the numbers blow up as you get far from the origin. So yes, floating point errors eat you when you get far enough out into the corner of a cube.


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