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Zeno RogueDeveloper's intention: A beautiful visualization feature!What the users share: A chaotic art generator! BREAK THE LIMITS! 🎨🔥<a href="https://mathstodon.xyz/tags/HyperRogue" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#HyperRogue</a> <a href="https://mathstodon.xyz/tags/RogueViz" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#RogueViz</a> <a href="https://mathstodon.xyz/tags/HyperbolicGeometry" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#HyperbolicGeometry</a> <a href="https://mathstodon.xyz/tags/NonEuclideanGeometry" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#NonEuclideanGeometry</a> <a href="https://mathstodon.xyz/tags/NonEuclidean" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#NonEuclidean</a>

Zeno RogueEvery tile in a hyperbolic tiling is randomly colored red or blue. How far should we move to find a specific pattern (a shape constructed out of tiles, with specific colors)?The distance is usually proportional to \(n\), the number of tiles in the pattern -- this is because at a given location the pattern appears with probability \( 1/2^n \), and there are \(\Theta(c^d)\) possible locations in distance d.So, for example, HyperRogue normally displays 582 tiles, and for every specific coloring of these 582 tiles, it should be somewhere in about 742 steps (and all of them in about 753 steps). If we used symbols (26 letters + space) instead of colors and were looking for a specific message of 1000 characters, it should appear in radius 6000.Problem: however, it is not clear how to find such a pattern (and whether it would be still true for a given pseudorandom generator). What it the most elegant coloring algorithm with similar properties but where requested patterns can be found by following some procedure? (If you do not know how hyperbolic geometry works, might be easier to think about binary trees)<a href="https://mathstodon.xyz/tags/NonEuclideanGeometry" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#NonEuclideanGeometry</a> <a href="https://mathstodon.xyz/tags/NonEuclidean" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#NonEuclidean</a> <a href="https://mathstodon.xyz/tags/HyperbolicGeometry" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#HyperbolicGeometry</a> <a href="https://mathstodon.xyz/tags/HyperRogue" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#HyperRogue</a> <a href="https://mathstodon.xyz/tags/roguelike" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#roguelike</a> <a href="https://mathstodon.xyz/tags/procgen" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#procgen</a>

Zeno RogueThe largest Christmas decoration in a videogame! <a href="https://mathstodon.xyz/tags/mathart" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#mathart</a> <a href="https://mathstodon.xyz/tags/noneuclidean" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#noneuclidean</a> <a href="https://mathstodon.xyz/tags/NoneuclideanGeometry" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#NoneuclideanGeometry</a> <a href="https://mathstodon.xyz/tags/roguelike" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#roguelike</a> <a href="https://mathstodon.xyz/tags/HyperRogue" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#HyperRogue</a>

Zeno RogueUsing hyperbolic geometry to create a weird musical instrument.The drawing tool in HyperRogue lets us to draw on the hyperbolic plane; we combine this with the scrolling animation. This scrolling animation makes the pen move on the surface -- the further we are from the central horizontal line, the faster it moves (a property of hyperbolic geometry); it should of course make some scratching sound when it is drawing, and the frequency of this sound should be proportional to its speed. Also we draw on the Klein quartic to make the display more interesting.<a href="https://mathstodon.xyz/tags/NonEuclidean" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#NonEuclidean</a> <a href="https://mathstodon.xyz/tags/NonEuclideanGeometry" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#NonEuclideanGeometry</a> <a href="https://mathstodon.xyz/tags/HyperRogue" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#HyperRogue</a> <a href="https://mathstodon.xyz/tags/RogueViz" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#RogueViz</a> <a href="https://mathstodon.xyz/tags/mathart" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#mathart</a>

Zeno RogueStill needs some improvements, but already available for some early access testing in HyperRogue 12.1x. HyperRogue 12.2 should be released soon!Here the arrows reflect in mirrors, and also we have some mimics, who shoot mimic arrows. Last seconds show that the arrows indeed fly in straight lines, even after reflecting off mirrors. <a href="https://mathstodon.xyz/tags/screenshotsaturday" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#screenshotsaturday</a> <a href="https://mathstodon.xyz/tags/HyperRogue" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#HyperRogue</a> <a href="https://mathstodon.xyz/tags/HyperbolicGeometry" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#HyperbolicGeometry</a>

GHyperRogue is a rogue like game made is mathematical formulas to create geometrical visuals that seamlessly fit together. Highly unusual looking.<a href="https://store.steampowered.com/app/342610/HyperRogue/" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://store.steampowered.com/app/342610/HyperRogue/</a>How it was done: <a href="http://roguetemple.com/z/hyper/dev.php" target="_blank" rel="nofollow noopener noreferrer" translate="no">http://roguetemple.com/z/hyper/dev.php</a><a href="https://mstdn.games/tags/HyperRogue" class="mention hashtag" rel="tag">#HyperRogue</a> <a href="https://mstdn.games/tags/RogueLike" class="mention hashtag" rel="tag">#RogueLike</a> <a href="https://mstdn.games/tags/Rogue" class="mention hashtag" rel="tag">#Rogue</a> <a href="https://mstdn.games/tags/geometry" class="mention hashtag" rel="tag">#geometry</a> <a href="https://mstdn.games/tags/game" class="mention hashtag" rel="tag">#game</a>

Dame-Armiger Kali Ranya ⚔️🐈A short break from Echo of Starsong, for something *weird*-- Tonight I'll be playing <a href="https://vtuber.house/tags/HyperRogue" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#HyperRogue</a>, a mind-bending Roguelike based in hyperbolic geometry! Where we're going, we'll never find our way back...<a href="https://twitch.tv/kaliranya" rel="nofollow noopener noreferrer" target="_blank">https://twitch.tv/kaliranya</a><a href="https://vtuber.house/tags/Streaming" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Streaming</a> <a href="https://vtuber.house/tags/LiveStream" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#LiveStream</a> <a href="https://vtuber.house/tags/KaLiveRa" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#KaLiveRa</a> <a href="https://vtuber.house/tags/ShareYourGames" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#ShareYourGames</a>

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