{"id":925,"date":"2025-08-25T12:12:06","date_gmt":"2025-08-25T09:12:06","guid":{"rendered":"https:\/\/users.utu.fi\/jkari\/?page_id=925"},"modified":"2025-12-31T10:44:36","modified_gmt":"2025-12-31T08:44:36","slug":"tilings2025","status":"publish","type":"page","link":"https:\/\/users.utu.fi\/jkari\/tilings2025\/","title":{"rendered":"Tilings and Patterns"},"content":{"rendered":"<div align=\"center\">\n<h3 style=\"text-align: center\">Fall term 2025<\/h3>\n<h3 style=\"text-align: center\"><span style=\"color: #ff0000\"><b>Tilings and Patterns<\/b><\/span><\/h3>\n<\/div>\n<p><span style=\"color: #808080\"><a style=\"color: #808080\" href=\"https:\/\/users.utu.fi\/jkari\/tilings2025-syllabus\/\" rel=\"\"><b>Course syllabus<\/b><\/a><\/span><\/p>\n<h4><span style=\"color: #000000\"><b>Some slides (pdf, best viewed in full screen mode): <\/b><\/span><\/h4>\n<ul>\n<li><span style=\"color: #808080\"><a style=\"color: #808080\" href=\"https:\/\/users.utu.fi\/jkari\/wp-content\/uploads\/sites\/1251\/2023\/08\/symmetry-compressed.pdf\"><b>General introduction to some topics of the course (mostly symmetries<\/b><\/a>)<\/span><\/li>\n<li><span style=\"color: #808080\"><b><a style=\"color: #808080\" href=\"https:\/\/users.utu.fi\/jkari\/wp-content\/uploads\/sites\/1251\/2021\/10\/threereflections.pdf\">Plane isometries are compositions of at most three reflections<\/a><\/b><\/span><\/li>\n<li><strong><span style=\"color: #808080\"><a style=\"color: #808080\" href=\"https:\/\/users.utu.fi\/jkari\/wp-content\/uploads\/sites\/1251\/2021\/10\/frieze.pdf\">Frieze group examples<\/a><\/span><\/strong><\/li>\n<li><strong><span style=\"color: #808080\"><a style=\"color: #808080\" href=\"https:\/\/users.utu.fi\/jkari\/wp-content\/uploads\/sites\/1251\/2021\/10\/hex.pdf\">Deriving the 17 wallpaper groups<\/a><\/span><\/strong><\/li>\n<li><span style=\"color: #808080\"><b><a style=\"color: #808080\" href=\"https:\/\/users.utu.fi\/jkari\/wp-content\/uploads\/sites\/1251\/2021\/10\/decisiontree1_eng.pdf\">Flowchart to determine wallpaper groups<\/a><\/b><\/span><\/li>\n<li><span style=\"color: #808080\"><strong><a style=\"color: #808080\" href=\"https:\/\/users.utu.fi\/jkari\/wp-content\/uploads\/sites\/1251\/2021\/10\/robinson.pdf\">Robinson&#8217;s aperiodic Wang tile set<\/a><\/strong><\/span><\/li>\n<li><span style=\"color: #808080\"><strong><a style=\"color: #808080\" href=\"https:\/\/users.utu.fi\/jkari\/wp-content\/uploads\/sites\/1251\/2021\/10\/wang14.pdf\">An aperiodic Wang tile set of 14 tiles<\/a><\/strong><\/span><\/li>\n<li><span style=\"color: #808080\"><a style=\"color: #808080\" href=\"https:\/\/users.utu.fi\/jkari\/wp-content\/uploads\/sites\/1251\/2021\/10\/dominoproblem-1.pdf\"><strong>On the undecidability of tiling problems<\/strong><\/a><\/span><\/li>\n<\/ul>\n<h4><b>Lecture Notes (pdf): <\/b><b><\/b><\/h4>\n<ul>\n<li><span style=\"color: #808080\"><strong><a style=\"color: #808080\" href=\"https:\/\/users.utu.fi\/jkari\/wp-content\/uploads\/sites\/1251\/2025\/09\/part1.pdf\">Part 1<\/a><\/strong><\/span><\/li>\n<li><strong><span style=\"color: #808080\"><a style=\"color: #808080\" href=\"https:\/\/users.utu.fi\/jkari\/wp-content\/uploads\/sites\/1251\/2025\/11\/fullnotes.pdf\">Part 1 + Part 2<\/a><\/span><\/strong><\/li>\n<\/ul>\n<h4><b>Lecture Slides (pdf):<\/b><\/h4>\n<ul>\n<li><span style=\"color: #808080\"><strong><a style=\"color: #808080\" href=\"https:\/\/users.utu.fi\/jkari\/wp-content\/uploads\/sites\/1251\/2025\/09\/lecture1.pdf\">Lecture Tuesday 9.9.2025<\/a><\/strong><\/span><\/li>\n<li><span style=\"color: #808080\"><strong><a style=\"color: #808080\" href=\"https:\/\/users.utu.fi\/jkari\/wp-content\/uploads\/sites\/1251\/2025\/09\/lecture2.pdf\">Lecture Thursday 11.9.2025<\/a><\/strong><\/span><\/li>\n<li><span style=\"color: #808080\"><strong><a style=\"color: #808080\" href=\"https:\/\/users.utu.fi\/jkari\/wp-content\/uploads\/sites\/1251\/2025\/09\/lecture3.pdf\">Lecture Tuesday 16.9.2025<\/a><\/strong><\/span><\/li>\n<li><span style=\"color: #808080\"><strong><a style=\"color: #808080\" href=\"https:\/\/users.utu.fi\/jkari\/wp-content\/uploads\/sites\/1251\/2025\/09\/lecture4.pdf\">Lecture Wednesday 17.9.2025<\/a><\/strong><\/span><\/li>\n<li><span style=\"color: #808080\"><strong><a style=\"color: #808080\" href=\"https:\/\/users.utu.fi\/jkari\/wp-content\/uploads\/sites\/1251\/2025\/09\/lecture5.pdf\">Lecture Thursday 18.9.2025<\/a><\/strong><\/span><\/li>\n<li><span style=\"color: #808080\"><strong><a style=\"color: #808080\" href=\"https:\/\/users.utu.fi\/jkari\/wp-content\/uploads\/sites\/1251\/2025\/09\/lecture6.pdf\">Lecture Tuesday 23.9.2025<\/a><\/strong><\/span><\/li>\n<li><span style=\"color: #808080\"><strong><a style=\"color: #808080\" href=\"https:\/\/users.utu.fi\/jkari\/wp-content\/uploads\/sites\/1251\/2025\/09\/lecture7.pdf\">Lecture Tuesday 30.9.2025<\/a><\/strong><\/span><\/li>\n<li><strong><span style=\"color: #808080\"><a style=\"color: #808080\" href=\"https:\/\/users.utu.fi\/jkari\/wp-content\/uploads\/sites\/1251\/2025\/10\/lecture8.pdf\">Lecture Thursday 2.10.2025<\/a><\/span><\/strong><\/li>\n<li><span style=\"color: #808080\"><strong><a style=\"color: #808080\" href=\"https:\/\/users.utu.fi\/jkari\/wp-content\/uploads\/sites\/1251\/2025\/10\/lecture9.pdf\">Lecture Tuesday 7.10.2025<\/a><\/strong><\/span><\/li>\n<li><strong><span style=\"color: #808080\"><a style=\"color: #808080\" href=\"https:\/\/users.utu.fi\/jkari\/wp-content\/uploads\/sites\/1251\/2025\/10\/lecture10.pdf\">Lecture Tuesday 14.10.2025<\/a><\/span><\/strong><\/li>\n<li><strong><span style=\"color: #808080\"><a style=\"color: #808080\" href=\"https:\/\/users.utu.fi\/jkari\/wp-content\/uploads\/sites\/1251\/2025\/10\/lecture11.pdf\">Lecture Wednesday 29.10.2025<\/a><\/span><\/strong><\/li>\n<li><strong><span style=\"color: #808080\"><a style=\"color: #808080\" href=\"https:\/\/users.utu.fi\/jkari\/wp-content\/uploads\/sites\/1251\/2025\/10\/lecture12.pdf\">Lecture Thursday 30.10.2025<\/a><\/span><\/strong><\/li>\n<li><span style=\"color: #808080\"><strong><a style=\"color: #808080\" href=\"https:\/\/users.utu.fi\/jkari\/wp-content\/uploads\/sites\/1251\/2025\/11\/lecture13.pdf\">Lecture Tuesday 4.11.2025<\/a><\/strong><\/span><\/li>\n<li><span style=\"color: #808080\"><strong><a style=\"color: #808080\" href=\"https:\/\/users.utu.fi\/jkari\/wp-content\/uploads\/sites\/1251\/2025\/11\/lecture14.pdf\">Lecture Wednesday 5.11.2025<\/a><\/strong><\/span><\/li>\n<li><span style=\"color: #808080\"><strong><a style=\"color: #808080\" href=\"https:\/\/users.utu.fi\/jkari\/wp-content\/uploads\/sites\/1251\/2025\/11\/lecture15.pdf\">Lecture Thursday 6.11.2025<\/a><\/strong><\/span><\/li>\n<li><span style=\"color: #808080\"><strong><a style=\"color: #808080\" href=\"https:\/\/users.utu.fi\/jkari\/wp-content\/uploads\/sites\/1251\/2025\/11\/lecture16.pdf\">Lecture Tuesday 11.11.2025<\/a><\/strong><\/span><\/li>\n<li><span style=\"color: #808080\"><strong><a style=\"color: #808080\" href=\"https:\/\/users.utu.fi\/jkari\/wp-content\/uploads\/sites\/1251\/2025\/11\/lecture17.pdf\">Lecture Tuesday 18.11.2025<\/a><\/strong><\/span><\/li>\n<li><span style=\"color: #808080\"><strong><a style=\"color: #808080\" href=\"https:\/\/users.utu.fi\/jkari\/wp-content\/uploads\/sites\/1251\/2025\/11\/lecture18.pdf\">Lecture Wednesday 19.11.2025<\/a><\/strong><\/span><\/li>\n<li><span style=\"color: #808080\"><strong><a style=\"color: #808080\" href=\"https:\/\/users.utu.fi\/jkari\/wp-content\/uploads\/sites\/1251\/2025\/11\/lecture19.pdf\">Lecture Thursday 20.11.2025<\/a><\/strong><\/span><\/li>\n<li><span style=\"color: #808080\"><a style=\"color: #808080\" href=\"https:\/\/users.utu.fi\/jkari\/wp-content\/uploads\/sites\/1251\/2025\/11\/lecture20.pdf\"><strong>Lecture Tuesday 25.11.2025<\/strong><\/a><\/span><\/li>\n<li><span style=\"color: #808080\"><strong><a style=\"color: #808080\" href=\"https:\/\/users.utu.fi\/jkari\/wp-content\/uploads\/sites\/1251\/2025\/11\/lecture21.pdf\">Lecture Thursday 27.11.2025<\/a><\/strong><\/span><\/li>\n<li><span style=\"color: #808080\"><strong><a style=\"color: #808080\" href=\"https:\/\/users.utu.fi\/jkari\/wp-content\/uploads\/sites\/1251\/2025\/12\/lecture22.pdf\">Lecture Tuesday 2.12.2025<\/a><\/strong><\/span><\/li>\n<li><span style=\"color: #808080\"><strong><a style=\"color: #808080\" href=\"https:\/\/users.utu.fi\/jkari\/wp-content\/uploads\/sites\/1251\/2025\/12\/lecture23.pdf\">Lecture Thursday 4.12.2025<\/a><\/strong><\/span><\/li>\n<\/ul>\n<h4><b>Homework Assignments (pdf):<\/b><\/h4>\n<ul>\n<li><span style=\"color: #808080\"><a style=\"color: #808080\" href=\"https:\/\/users.utu.fi\/jkari\/wp-content\/uploads\/sites\/1251\/2025\/08\/homework1.pdf\"><b>Homework 1<\/b><\/a> (15.9.2025)<\/span><\/li>\n<li><span style=\"color: #808080\"><strong><a style=\"color: #808080\" href=\"https:\/\/users.utu.fi\/jkari\/wp-content\/uploads\/sites\/1251\/2025\/09\/homework2.pdf\">Homework 2<\/a> <\/strong>(22.9.2025)<\/span><\/li>\n<li><span style=\"color: #808080\"><strong><a style=\"color: #808080\" href=\"https:\/\/users.utu.fi\/jkari\/wp-content\/uploads\/sites\/1251\/2025\/09\/homework3.pdf\">Homework 3<\/a> <\/strong>(29.9.2025)<\/span><\/li>\n<li><span style=\"color: #808080\"><a style=\"color: #808080\" href=\"https:\/\/users.utu.fi\/jkari\/wp-content\/uploads\/sites\/1251\/2025\/09\/homework4.pdf\"><strong>Homework 4<\/strong><\/a> (6.10.2025)<\/span><\/li>\n<li><span style=\"color: #808080\"><strong><a style=\"color: #808080\" href=\"https:\/\/users.utu.fi\/jkari\/wp-content\/uploads\/sites\/1251\/2025\/10\/homework5.pdf\">Homework 5<\/a><\/strong> (<\/span><span style=\"color: #808080\">13.10.2025)<\/span><\/li>\n<li><span style=\"color: #808080\"><a style=\"color: #808080\" href=\"https:\/\/users.utu.fi\/jkari\/wp-content\/uploads\/sites\/1251\/2025\/10\/homework6.pdf\"><strong>Homework 6<\/strong><\/a> (16.10.2025)<\/span><\/li>\n<li><span style=\"color: #808080\"><a style=\"color: #808080\" href=\"https:\/\/users.utu.fi\/jkari\/wp-content\/uploads\/sites\/1251\/2025\/10\/homework7.pdf\"><strong>Homework 7<\/strong><\/a> (3.11.2025)<\/span><\/li>\n<li><span style=\"color: #808080\"><strong><a style=\"color: #808080\" href=\"https:\/\/users.utu.fi\/jkari\/wp-content\/uploads\/sites\/1251\/2025\/11\/homework8.pdf\">Homework 8<\/a><\/strong> (10.11.2025)<\/span><\/li>\n<li><span style=\"color: #808080\"><strong><a style=\"color: #808080\" href=\"https:\/\/users.utu.fi\/jkari\/wp-content\/uploads\/sites\/1251\/2025\/11\/homework9.pdf\">Homework 9<\/a><\/strong> (17.11.2025)<\/span><\/li>\n<li><span style=\"color: #808080\"><strong><a style=\"color: #808080\" href=\"https:\/\/users.utu.fi\/jkari\/wp-content\/uploads\/sites\/1251\/2025\/11\/homework10.pdf\">Homework 10<\/a><\/strong> (24.11.2025)<\/span><\/li>\n<li><span style=\"color: #808080\"><strong><a style=\"color: #808080\" href=\"https:\/\/users.utu.fi\/jkari\/wp-content\/uploads\/sites\/1251\/2025\/11\/homework11.pdf\">Homework 11<\/a><\/strong> (1.12.2025)<\/span><\/li>\n<li><span style=\"color: #808080\"><strong><a style=\"color: #808080\" href=\"https:\/\/users.utu.fi\/jkari\/wp-content\/uploads\/sites\/1251\/2025\/11\/homework12.pdf\">Homework 12<\/a><\/strong> (8.12.2025)<\/span><\/li>\n<li><span style=\"color: #808080\"><a style=\"color: #808080\" href=\"https:\/\/users.utu.fi\/jkari\/wp-content\/uploads\/sites\/1251\/2025\/12\/homework13.pdf\"><strong>Homework 13<\/strong><\/a> (11.12.2025)<\/span><\/li>\n<\/ul>\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Fall term 2025 Tilings and Patterns Course syllabus Some slides (pdf, best viewed in full screen mode): General introduction to some topics of the course (mostly symmetries) Plane isometries are compositions of at most three reflections Frieze group examples Deriving the 17 wallpaper groups Flowchart to determine wallpaper groups Robinson&#8217;s aperiodic Wang tile set An&hellip; <a class=\"more-link\" href=\"https:\/\/users.utu.fi\/jkari\/tilings2025\/\">Continue reading <span class=\"screen-reader-text\">Tilings and Patterns<\/span><\/a><\/p>\n","protected":false},"author":6330,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-925","page","type-page","status-publish","hentry","entry"],"_links":{"self":[{"href":"https:\/\/users.utu.fi\/jkari\/wp-json\/wp\/v2\/pages\/925","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/users.utu.fi\/jkari\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/users.utu.fi\/jkari\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/users.utu.fi\/jkari\/wp-json\/wp\/v2\/users\/6330"}],"replies":[{"embeddable":true,"href":"https:\/\/users.utu.fi\/jkari\/wp-json\/wp\/v2\/comments?post=925"}],"version-history":[{"count":72,"href":"https:\/\/users.utu.fi\/jkari\/wp-json\/wp\/v2\/pages\/925\/revisions"}],"predecessor-version":[{"id":1102,"href":"https:\/\/users.utu.fi\/jkari\/wp-json\/wp\/v2\/pages\/925\/revisions\/1102"}],"wp:attachment":[{"href":"https:\/\/users.utu.fi\/jkari\/wp-json\/wp\/v2\/media?parent=925"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}