0:00 Getting Close This looks like a platformer from the 80's... but there is something strange about it. A rather subtle thing. Can you see this in this video? You may have noticed that the guy gets smaller the higher we go. Also the height of his jump appears smaller. 0:12 Climbing the Tower Let's climb this narrow tower to see this better... It is not really the guy getting smaller, but rather the world getting bigger! The guy is always the same size and has the same jump height. But that tower gets wider and wider. 0:40 Big Jump OK, it seems we cannot climb this tower any higher. So let's see what happens when we jump. What's going on?... Well, it takes place in a world with hyperbolic geometry. The cool thing about non-Euclidean geometry is that looks quite normal on the first glance but is actually very weird (contrary to so-called non-Euclidean games which appear weird but are not really that weird). 1:06 Big Jump explained The videos were taken in the lower half-plane model (the boundary line is one screen above the top line of the video). But here is our big jump, shown in the Poincaré disk model. We actually fall almost strictly downwards... but then, the straight almost vertical line "misses" the ground, and we continue our fall upwards! 1:11 Base in the disk model Here is the base of the tower in Poincaré disk model. (Some interesting moire patterns by the way.) 1:16 Our Inspiration This visualization takes inspiration from Jet Set Willy. Miner Willy's house in Jet Set Willy is a bit weird: 4 rooms on the top floor are as wide as 6 floors on the roof, and 9 rooms on the first floor are as wide as 3 rooms on the basement. What if we did this thing but more consistently? No plans to continue working on this prototype at the moment, but the source code can be found in: https://github.com/zenorogue/hyperrogue/blob/master/rogueviz/platformer.cpp (and tried in RogueViz) This design could be good in a platformer based on exploration, for example, a metroidvania-style platformer, where we could easily reach exponential area without using any kinds of quick transport, or in a procedurally generated platformer in the style of Terraria. People try to create a non-Euclidean minecraft-like (Ralith's Hypermine/kayturs's HyperBlock), but by the state of these projects, it sounds it is a much more difficult project than it seems. This one should be easier. Still exponential world, larger than anything Euclidean... Music used: * "Lost Mountain" from the HyperRogue Soundtrack by Lincoln Domina, CC 4.0, and * Jet Set Willy soundtrack from the PC remake of Jet Set Willy (original JSW by Matthew Smith, PC remake by Andy Noble, music by Matt Simmonds) Map of the ZX Spectrum version of Jet Set Willy taken from: https://maps.speccy.cz/map.php?id=JetSetWilly1 Previously shown on Twitter: https://twitter.com/ZenoRogue/status/1467233261801951232 Have fun!