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Constraints JournalHappy Monday everyone!Here's something to brighten up the start of your week: a paper about solving mathemusical problems with ILP and SAT, from our latest issue:Computing aperiodic tiling rhythmic canons via SAT models <a href="https://link.springer.com/article/10.1007/s10601-024-09375-6" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://link.springer.com/article/10.1007/s10601-024-09375-6</a>To make this Monday extra sweet: the authors use MapleSAT!<a href="https://mastodon.acm.org/tags/Mathematics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Mathematics</a> <a href="https://mastodon.acm.org/tags/Music" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Music</a> <a href="https://mastodon.acm.org/tags/ConstraintProgramming" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#ConstraintProgramming</a> <a href="https://mastodon.acm.org/tags/AI" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#AI</a> <a href="https://mastodon.acm.org/tags/Rhythm" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Rhythm</a> <a href="https://mastodon.acm.org/tags/AcademicMastodon" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#AcademicMastodon</a> <a href="https://mastodon.acm.org/tags/BooleanSatisfiability" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#BooleanSatisfiability</a> <a href="https://mastodon.acm.org/tags/AperiodicTiling" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#AperiodicTiling</a> <a href="https://mastodon.acm.org/tags/MapleSAT" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#MapleSAT</a> <a href="https://mastodon.acm.org/tags/ILP" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#ILP</a> <a href="https://mastodon.acm.org/tags/CombinatorialAlgorithms" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#CombinatorialAlgorithms</a> <a href="https://mastodon.acm.org/tags/ArtificialIntelligence" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#ArtificialIntelligence</a>

Deborah PickettStarting the next <a href="https://old.mermaid.town/tags/quilting" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#quilting</a> project. <a href="https://old.mermaid.town/tags/hat" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#hat</a> <a href="https://old.mermaid.town/tags/textiles" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#textiles</a> <a href="https://old.mermaid.town/tags/FiberArts" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#FiberArts</a> <a href="https://old.mermaid.town/tags/geometry" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#geometry</a> <a href="https://old.mermaid.town/tags/tessellation" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#tessellation</a> <a href="https://old.mermaid.town/tags/AperiodicTiling" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#AperiodicTiling</a>

Craig SailaHere's a more detailed article on the recently discovered non-repeating "einstein" shape — covers a lot more about the <a href="https://mastodon.social/tags/design" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#design</a> of <a href="https://mastodon.social/tags/AperiodicTiling" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#AperiodicTiling</a>, why <a href="https://mastodon.social/tags/The" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#The</a> Hat works, and how it was tested <a href="https://www.scientificamerican.com/article/newfound-mathematical-einstein-shape-creates-a-never-repeating-pattern/" rel="nofollow noopener noreferrer" target="_blank">https://www.scientificamerican.com/article/newfound-mathematical-einstein-shape-creates-a-never-repeating-pattern/</a>

Craig Saila<a href="https://mastodon.social/tags/Design" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Design</a> meets <a href="https://mastodon.social/tags/math" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#math</a>: A geometric shape that doesn't repeat itself when tiled may finally have been discovered — and its referred to as an 'einstein" shape, but not for the reasons you might guess<a href="https://mastodon.social/tags/TheHat" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#TheHat</a> <a href="https://mastodon.social/tags/AperiodicTiling" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#AperiodicTiling</a> <a href="https://mastodon.social/tags/pattern" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#pattern</a> <a href="https://phys.org/news/2023-03-geometric-tiled.html" rel="nofollow noopener noreferrer" target="_blank">https://phys.org/news/2023-03-geometric-tiled.html</a>

Ivan Enderlin 🦀An aperiodic monotile, <a href="https://arxiv.org/abs/2303.10798" rel="nofollow noopener noreferrer" target="_blank">https://arxiv.org/abs/2303.10798</a>.This is so awesome.<a href="https://fosstodon.org/tags/tiling" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#tiling</a> <a href="https://fosstodon.org/tags/AperiodicTiling" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#AperiodicTiling</a> <a href="https://fosstodon.org/tags/polyform" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#polyform</a>

notsoloudAround here, the brand new <a href="https://expressional.social/tags/aperiodictiling" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#aperiodictiling</a> is already out as a puzzle!Hoping to get the colored version going soon!For more info <a href="https://cs.uwaterloo.ca/~csk/hat/" rel="nofollow noopener noreferrer" target="_blank">https://cs.uwaterloo.ca/~csk/hat/</a><a href="https://expressional.social/tags/laserCutter" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#laserCutter</a> <a href="https://expressional.social/tags/making" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#making</a>

Karthik SrinivasanWow!! What a breathe of fresh air this paper is in the midst of suffocating levels of "AI solves everything" hype cycle. <a href="https://arxiv.org/abs/2303.10798" rel="nofollow noopener noreferrer" target="_blank">https://arxiv.org/abs/2303.10798</a>They have found at long last, a single tile, an "einstein", which they call a "hat"/polykite that tiles the entire plane aperiodically. Previously the best known aperiodic tiling of the plane required at the least two different tiles, the most famous ones being the Penrose tiles, and those that adorn Alhambra. It is all the more wonderful that the first two authors don't have any academic/research affiliations. They write somewhere in the paper, how it all started, so wonderful: "One of the authors (Smith) began investigating the hat polykite as part of his open-ended visual exploration of shapes and their tiling properties. Working largely by hand, with the assistance of Scherphuis’s PolyForm Puzzle Solver software (<a href="http://www.jaapsch.net/puzzles/polysolver.htm" rel="nofollow noopener noreferrer" target="_blank">www.jaapsch.net/puzzles/polysolver.htm</a>), he could find no obvious barriers to the construction of large patches, and yet no clear cluster of tiles that filled the plane periodically." Why is the study of tilings such a big deal? Well, it hints at and tries to formalize various physics concepts that are of immense interest to many of us (and dare I say, even neuroscientists): quasi crystals!, possible new states of matter, emergent structures from simple units, how symmetries and asymmetries arise, stability of heterogenous media, soft matter physics, order without periodicity, criticality etc., etc., On quasi-crystals and their search, applications, uses etc., I recommend the wonderful Paul Steinhardt's book: "The Second Kind of Impossible: The Extraordinary Quest for a New Form of Matter" <a href="https://neuromatch.social/tags/Physics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Physics</a> <a href="https://neuromatch.social/tags/Maths" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Maths</a> <a href="https://neuromatch.social/tags/Combinatorics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Combinatorics</a> <a href="https://neuromatch.social/tags/AperiodicTiling" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#AperiodicTiling</a> <a href="https://neuromatch.social/tags/PenroseTiles" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#PenroseTiles</a> <a href="https://neuromatch.social/tags/Einstein" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Einstein</a> <a href="https://neuromatch.social/tags/Emergence" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Emergence</a> <a href="https://neuromatch.social/tags/condensedmatter" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#condensedmatter</a>

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