Zeno Rogue

@ZenoRogue

Mathematics, game development, art, roguelikes, hyperbolic geometry. Sometimes all at once.

roguetemple.com/z
Joined June 2012
513 Photos and videos Photos and videos

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  1. Pinned Tweet
    18 Jun 2019

    HyperRogue version 11.1 released! 3D geometries, 3D view of 2D geometries, and new special modes.

    5 replies 17 retweets 130 likes
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  2. Retweeted
    2 hours ago

    NovaMundi: The Spear of Chaquén, is coming to on April 13, 2021, and we have a new trailer to celebrate! With your help, the Muisca will rise united. Remember to wishlist if you like it!

    1 reply 6 retweets 6 likes
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  3. Mar 22

    In spherical geometry, you would see the back of your head. Everywhere, unless your view was blocked by something else! So far this aspect has been AFAIK always left to the reader's imagination, so let's change that. (More in )

    5 replies 10 retweets 24 likes
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  4. Mar 20

    Let's try a knot portal, based on a trefoil knot. Hard to grasp this. It is "self-hiding" -- in some worlds the portal is not there -- but it may still appear to be there, because the light will travel around the sphere and hit the copy of the portal in another world. (4/4)

    1 reply 4 retweets 17 likes
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  5. Mar 20

    Here we change the geometry a bit (the Berger sphere). This way, we see several lone bricks at once, instead of seeing only two (and the other four being hidden by their counterparts in closer worlds). (3/4)

    2 replies 16 likes
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  6. Mar 20

    The same scene with a bit different perspective. These videos use 270° field of view (obtained with the stereographic projection), so the ring would be actually seen around you. With a small field-of-view, there would be no way to see the whole ring at once. (2/4)

    1 reply 12 likes
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  7. Mar 20

    Another non-Euclidean portal! This one is a great circle in the three-dimensional spherical space. It connects six worlds, each with different fog colors and a different color of the "lone brick". (1/4)

    6 replies 19 retweets 96 likes
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  8. Retweeted
    Mar 19

    Also, the Triple portal generates a very beautiful where parts pointed towards each other.

    1 reply 1 retweet 27 likes
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  9. Mar 18

    A non-Euclidean portal, shaped like a Penrose staircase in Nil geometry.

    8 replies 57 retweets 251 likes
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  10. Mar 18

    There is no obvious reason why every finite connected vertex-transitive graph should contain a Hamiltonian path, but it seems to be true so far. László Lovász and Avi Wigderson win the Abel Prize. Congrats!

    2 replies 20 retweets 119 likes
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  11. Mar 16

    If you have no access to the 15+4 puzzle by yet, here is a virtual version:

    4 replies 19 retweets 53 likes
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  12. Retweeted
    Mar 15

    With Clang 13, you can literally format your hard drive, using C++ undefined behavior.

    A screenshot of the Compiler Explorer website, showing a C++ program and its compiled outputs.
    26 replies 268 retweets 861 likes
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  13. Mar 15

    Here the formulas are: x(a+t)=x(a)-ty(a), y(a+t)=y(a)+tx(a+t). In the limit, this is periodic with period 2π. For t=1 this is periodic with period 6, so the "discrete analog" of π would be 3.

    1 reply 1 retweet 14 likes
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  14. Mar 15

    A population of yaks grows according to the formula y(a+t)=y(a)+t·y(a). What is y(1) if y(0)=1? For very small t we get y(1)→e, but for t=1 we get y(1)=2. This makes 2 the "discrete analog" of e. What would be the discrete analog of π?

    4 replies 5 retweets 18 likes
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  15. Retweeted
    Mar 7

    Fun fact: if you open this image in full-size, you can't see it anymore.

    61 replies 2,283 retweets 6,119 likes
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  16. Mar 4

    Three-point equidistant projection of the order-3 dodecahedral honeycomb in ℍ³. Distances from three points are mapped faithfully; this is not always possible or unique, so the projection is not continuous.

    2 replies 2 retweets 35 likes
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  17. Feb 21

    An even more weird self-hiding portal:

    An even weirder knot portal. This time, from some viewpoints, it appears that some parts of the knot are not in the room we are currently in. We see all the knot in the first scene, and in the last scene, some part of the knot portal is hidden by itself.
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    2 retweets 8 likes
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  18. Feb 21

    The previous knot portal: and an improved video of it:

    1:33
    A knot portal made of blocks. The idea of a knot portal is not new -- you can play the beautiful KnotPortal by based on the idea of Bill Thurston: although the algorithms we have used here seem to be significantly different from KnotPortal.
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  19. Feb 21

    An even weirder knot portal. This time, from some viewpoints, it appears that some parts of the knot are not in the room we are currently in. We see all the knot in the first scene, and in the last scene, some part of the knot portal is hidden by itself.

    3 replies 5 retweets 25 likes
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  20. Feb 19

    An improved version: (reflective walls, more space around the portal, fixed a bug with the coloring of the knot)

    3 replies 4 retweets 19 likes
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  21. Feb 18

    A knot portal made of blocks. The idea of a knot portal is not new -- you can play the beautiful KnotPortal by based on the idea of Bill Thurston: although the algorithms we have used here seem to be significantly different from KnotPortal.

    18 replies 84 retweets 324 likes
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