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#mathviz

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Zeno Rogue<p>We cannot tell how fast we are moving (for example, do not feel that Earth is moving very fast). This is related to how the objects move at constant speed in a straight line if no force is acting on them.</p><p>This is not the case in spherical or hyperbolic geometry, though (assuming a naive model of time*). In this visualization, every point in the yellowish &quot;ghost&quot; moves in a straight line at constant speed. The captain could tell how fast they are moving by measuring these distortions.</p><p>* not the case in (anti-)de Sitter spacetime, as in Relative Hell. <a href="https://zenorogue.itch.io/relative-hell" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">zenorogue.itch.io/relative-hel</span><span class="invisible">l</span></a></p><p><a href="https://mathstodon.xyz/tags/NonEuclideanGeometry" class="mention hashtag" rel="tag">#<span>NonEuclideanGeometry</span></a> <a href="https://mathstodon.xyz/tags/NonEuclidean" class="mention hashtag" rel="tag">#<span>NonEuclidean</span></a> <a href="https://mathstodon.xyz/tags/mathart" class="mention hashtag" rel="tag">#<span>mathart</span></a> <a href="https://mathstodon.xyz/tags/mathviz" class="mention hashtag" rel="tag">#<span>mathviz</span></a></p>
Zeno Rogue<p>Our new video! We take you on a journey through a small game world and showcase the non-Euclidean transformations of its third dimension.</p><p>Full video on YouTube: <a href="https://youtu.be/Rhjv_PazzZE" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="">youtu.be/Rhjv_PazzZE</span><span class="invisible"></span></a> <a href="https://mathstodon.xyz/tags/noneuclidean" class="mention hashtag" rel="tag">#<span>noneuclidean</span></a> <a href="https://mathstodon.xyz/tags/mathart" class="mention hashtag" rel="tag">#<span>mathart</span></a> <a href="https://mathstodon.xyz/tags/mathviz" class="mention hashtag" rel="tag">#<span>mathviz</span></a> <a href="https://mathstodon.xyz/tags/NoneuclideanGeometry" class="mention hashtag" rel="tag">#<span>NoneuclideanGeometry</span></a> <a href="https://mathstodon.xyz/tags/rogueviz" class="mention hashtag" rel="tag">#<span>rogueviz</span></a></p>
Zeno Rogue<p>Some <a href="https://mathstodon.xyz/tags/mathart" class="mention hashtag" rel="tag">#<span>mathart</span></a> from 2001.</p><p>Typical visualizations of surfaces I would see back then were boring, angular, and sameish -- they used the same default Mathematica colors, and the polygons were visible. (Google image &quot;Mathematica surface graph&quot; to find this style.)</p><p>Just like these typical graphs, this rendering method is based on triangles; however, as long as the triangles had &gt;1 pixel, they are recursively subdivided -- and eventually single pixels are colored according to a formula.</p><p><a href="https://mathstodon.xyz/tags/mathviz" class="mention hashtag" rel="tag">#<span>mathviz</span></a></p>
Zeno Rogue<p>If they expand in the same &#39;z&#39; direction, but with different rates instead, it looks more like a horosphere (compare the first visualization in this thread); this is why hexes in the visualization below are squished when we look at them orthogonally from far away. <a href="https://mathstodon.xyz/tags/mathart" class="mention hashtag" rel="tag">#<span>mathart</span></a> <a href="https://mathstodon.xyz/tags/noneuclidean" class="mention hashtag" rel="tag">#<span>noneuclidean</span></a> <a href="https://mathstodon.xyz/tags/hyperrogue" class="mention hashtag" rel="tag">#<span>hyperrogue</span></a> <a href="https://mathstodon.xyz/tags/rogueviz" class="mention hashtag" rel="tag">#<span>rogueviz</span></a> <a href="https://mathstodon.xyz/tags/mathviz" class="mention hashtag" rel="tag">#<span>mathviz</span></a> <a href="https://mathstodon.xyz/tags/visualization" class="mention hashtag" rel="tag">#<span>visualization</span></a></p>
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