Hyperbolix | 100% Pen Find your way through the hyperbolic plane, a strange space where nothing is as it seems. Unlock the mysteries of several challenging levels, while discovering the unique game mechanics and returning home. Getting through the intricate mazes and complex puzzles is not an easy task. It is your only chance of finding your way out, though. Can you return to your ordinary, flat plane? _____________________________________________ HOW TO PLAY At first glance, Hyperbolix looks like an ordinary scrolling platformer. The arrow keys or WASD are used to move a player through the world. Restart with R. However, an interesting feature exists. As you play, you'll notice that something is off... Once you notice this, your gameplay changes. Specifically, this game occurring on the hyper- bolic plane can help you realize the level structure. Work out other tricks of this space, and the path to victory is clear. _____________________________________________ HOW IT WORKS Those of you who have an aversion to mathematics may skip this section. If you want to understand the inner workings of this game, read on. A hyperbolic plane is a 2D plane with negative curvature. Therefore, two perpendicular axes set on it will have opposite signs. Examples of these surfaces are Pringles, or saddles. They can be visualized with the revolutionary hyperbolic crochet, invented by Daina Taimina. See https://www.stewardschool.org/file/bil/IFF-CrochetReef-HowToHandout-1-2.pdf for examples. Hyperbolae tend to maximize area, so a plane that has a small size could be extremely heavy. Because of this, Hyperbolix can fit a mind-blowing amount of level into the unit circle. To render these planes, they must be projected from 3D to 2D. Orthographic/isotopic projection is not useful, because the level would not shrink to the appropriate size. The stereographic, or Poincare disk mapping, is a better choice; however, it is conformal. This makes lines project to circles, and slows down rendering. The best choice is the gnomonic projection, also known as the Beltrami-Cayley-Klein projection. It is nonconformal, so it maps lines to lines. _____________________________________________ HOW TO CONTRIBUTE Liked this game? You can help in the following ways: - Communicating it to your friends - Suggesting new ideas in the comments - Commenting your favorite level and why - Leaving feedback - Adding it to your studios % .5k-blocks
