Monday, 26 October 2015

a paper model of the world of HyperRogue

After looking at some hyperbolic footballs, we have decided to make a paper model of a part of the world of HyperRogue! Such a model should give us some insight about how to imagine this world.

 
This is the HyperRogue scene that the model is based on. The model represents all the cells within radius 3 from the player character, which is 50 cells (35 hexagons and 15 heptagons). It appears curved because of the negative curvature of the hyperbolic plane -- the perimeter of a circle grows exponentially with its radius, not linearly as is common in the Euclidean world, so the edge has to twist a lot to fit everything, and the larger the model, the more curved it becomes. I was afraid that a larger region could be harder to fit in Euclidean space, or require too much work to complete, but probably one or two layers more would still be fine.

Based on the scene, HyperRogue rendered the net above. Print the net on four pages, cut out all the shapes, and glue the white triangles together — letters say which white triangle should be glued to which one -- actually, we have been using a small stapler for this, not glue. If I recall correctly, 85 pairs of white triangles had to be stapled.

This is how the model looks in motion.

If you would like to create your own model of your favorite land in HyperRogue, the next version of HyperRogue is going to create a net for you, based on the current scene around the player character! At the moment, HyperRogue is only programmed to create a net for 50 cells around the player on a heptagon -- of course, as we already know, the 50 cell pattern tiles the hyperbolic plane, so maybe one could create larger models simply by gluing the fifty-cell models together?

Have fun!

UPDATE: HyperRogue 8.0 has this feature -- please post a comment on the Steam forum, YouTube, or this blog if you make your own models! :)

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