{"id":206441,"date":"2025-02-14T14:18:05","date_gmt":"2025-02-14T20:18:05","guid":{"rendered":"https:\/\/lifeboat.com\/blog\/2025\/02\/the-einstein-problem-molecular-chirality-leads-to-unexpected-aperiodic-patterns-on-metal-surfaces"},"modified":"2025-02-14T14:18:05","modified_gmt":"2025-02-14T20:18:05","slug":"the-einstein-problem-molecular-chirality-leads-to-unexpected-aperiodic-patterns-on-metal-surfaces","status":"publish","type":"post","link":"https:\/\/lifeboat.com\/blog\/2025\/02\/the-einstein-problem-molecular-chirality-leads-to-unexpected-aperiodic-patterns-on-metal-surfaces","title":{"rendered":"The einstein problem: Molecular chirality leads to unexpected aperiodic patterns on metal surfaces"},"content":{"rendered":"<p><a class=\"aligncenter blog-photo\" href=\"https:\/\/lifeboat.com\/blog.images\/the-einstein-problem-molecular-chirality-leads-to-unexpected-aperiodic-patterns-on-metal-surfaces.jpg\"><\/a><\/p>\n<p>Standing at the intersection between mathematics and the tiler\u2019s trade is the so-called einstein problem. Despite its name, this mathematical question has nothing to do with the Nobel Prize winner Albert Einstein. It asks: Can you seamlessly tile an endless surface with a single shape (an \u201ceinstein\u201d) in such a way that the resulting pattern is never repeated? Such a \u201cproto-tile\u201d was first discovered in 2022 by the English amateur mathematician David Smith.<\/p>\n<p>Empa researcher Karl-Heinz Ernst is neither a mathematician nor a tiler. As a chemist, he researches the crystallization of molecules on <a href=\"https:\/\/phys.org\/tags\/metal+surfaces\/\" rel=\"tag\" class=\"\">metal surfaces<\/a>. He never expected to deal with the einstein problem in his professional life\u2014until his doctoral student Jan Voigt approached him with the unusual results of an experiment.<\/p>\n<p>When a certain molecule crystallized on a <a href=\"https:\/\/phys.org\/tags\/silver+surface\/\" rel=\"tag\" class=\"\">silver surface<\/a>, instead of the expected regular structure, irregular patterns were formed that never seemed to repeat themselves. Even more surprising: Each time he repeated the experiment, different aperiodic patterns emerged.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Standing at the intersection between mathematics and the tiler\u2019s trade is the so-called einstein problem. Despite its name, this mathematical question has nothing to do with the Nobel Prize winner Albert Einstein. It asks: Can you seamlessly tile an endless surface with a single shape (an \u201ceinstein\u201d) in such a way that the resulting pattern [\u2026]<\/p>\n","protected":false},"author":661,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2229],"tags":[],"class_list":["post-206441","post","type-post","status-publish","format-standard","hentry","category-mathematics"],"_links":{"self":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/posts\/206441","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/users\/661"}],"replies":[{"embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/comments?post=206441"}],"version-history":[{"count":0,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/posts\/206441\/revisions"}],"wp:attachment":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/media?parent=206441"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/categories?post=206441"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/tags?post=206441"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}