4 Dimensional Quaternions, Hyperspheres and Stereographic Space

I’ve been learning some mind bending maths with the help of the amazing tuturials and tools over here (based on threeJS I think:

It got me thinking about an idea I had years ago about making a virtual world which was M.C. Esher-like insofar as it didn’t stick to 3 dimensions or at least it used illusory space to mess with dimensions.

I can’t think of ayone who has done this before in a creative context (websites, games, art etc) and thought I’d ask over here if anyone had ever seen such a thing?


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I really appreciate your creative and “out-of-the-box” thinking. And very well presented with an inspiring illustration. But I’m afraid, most around here (including myself) are challenged already with the concept of 3D-quaternions.

Besides, visualizing 4D using a 3D-API, which ultimately gets projected onto 2D seems to be quite a - ahum - challenge. Which makes me interested in your progress so much more.

A stereographic space on the other hand is both conceptually much easier to grasp, as well as lending itself to immediate application by mere 3D-carbon-based lifeforms. :nerd_face:

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My favorite four-dimensional game is Miegakure. Here’s an explanation video of how it works:

And this guy builds a rendering engine using hyperbolic and spherical space, instead of the traditional Euclidean space:

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