{"id":493,"date":"2023-08-27T11:28:49","date_gmt":"2023-08-27T08:28:49","guid":{"rendered":"https:\/\/users.utu.fi\/jkari\/?page_id=493"},"modified":"2025-08-25T11:18:04","modified_gmt":"2025-08-25T08:18:04","slug":"tilings2023","status":"publish","type":"page","link":"https:\/\/users.utu.fi\/jkari\/tilings2023\/","title":{"rendered":"Tilings and Patterns 2023"},"content":{"rendered":"<div align=\"center\">\n<h3 style=\"text-align: center\">Fall term 2023<\/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\/tilings2023-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\">Flow chart to determine wall paper 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\/2023\/09\/toc.pdf\">Table of contents (parts 1&amp;2)<\/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\/2023\/09\/part1.pdf\">Part 1<\/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\/2023\/09\/part2.pdf\">Part 2<\/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\/2023\/11\/part3a.pdf\">Part 3(a)<\/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\/05\/part3b.pdf\">Part 3(b)<\/a><\/strong><\/span><\/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\/2023\/08\/lecture-2.pdf\">Lecture 30.8.<\/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\/2023\/08\/lecture-3.pdf\">Lecture 31.8.<\/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\/2023\/09\/lecture-4.pdf\">Lecture 5.9.<\/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\/2023\/09\/lecture-5.pdf\">Lecture 6.9.<\/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\/2023\/09\/lecture-6.pdf\">Lecture 7.9.<\/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\/2023\/09\/lecture-9.pdf\">Lecture 14.9.<\/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\/2023\/09\/lecture-10.pdf\"><strong>Lecture 19.9.<\/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\/2023\/09\/lecture-11.pdf\">Lecture 20.9.<\/a><\/strong><\/span><strong><span style=\"color: #808080\"><br \/>\n<\/span><\/strong><\/li>\n<li><span style=\"color: #808080\"><a style=\"color: #808080\" href=\"https:\/\/users.utu.fi\/jkari\/wp-content\/uploads\/sites\/1251\/2023\/09\/lecture-14.pdf\"><strong>Lecture 27.9.<\/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\/2023\/09\/lecture-15.pdf\">Lecture 28.9.<\/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\/2023\/10\/lecture-16.pdf\">Lecture 3.10.<\/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\/2023\/10\/lecture-17.pdf\">Lecture 4.10.<\/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\/2023\/10\/lecture-18.pdf\">Lecture 24.10.<\/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\/2023\/10\/lecture-19.pdf\">Lecture 26.10.<\/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\/2023\/10\/lecture-20.pdf\">Lecture 31.10.<\/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\/2023\/11\/lecture-21.pdf\">Lecture 1.11.<\/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\/2023\/11\/lecture-22.pdf\">Lecture 2.11.<\/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\/2023\/11\/lecture-23.pdf\"><strong>Lecture 14.11.<\/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\/2023\/11\/lecture-24.pdf\">Lecture 28.11.<\/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\/2023\/11\/lecture-25.pdf\">Lecture 29.11.<\/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\/2023\/12\/last-lectures.pdf\">Last lectures<\/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\/2023\/08\/homework1.pdf\"><b>Homework 1<\/b> (4.9.2023)<\/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\/2023\/09\/homework2.pdf\">Homework 2<\/a><\/strong><a style=\"color: #808080\" href=\"https:\/\/users.utu.fi\/jkari\/wp-content\/uploads\/sites\/1251\/2023\/09\/homework2.pdf\"> (11.9.2023)<\/a>\u00a0<\/span><\/li>\n<li><span style=\"color: #808080\"><a style=\"color: #808080\" href=\"https:\/\/users.utu.fi\/jkari\/wp-content\/uploads\/sites\/1251\/2023\/09\/homework3.pdf\"><strong>Homework 3 <\/strong>(18.9.2023)<\/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\/2023\/09\/homework4.pdf\">Homework 4 <\/a><\/strong><a style=\"color: #808080\" href=\"https:\/\/users.utu.fi\/jkari\/wp-content\/uploads\/sites\/1251\/2023\/09\/homework4.pdf\">(25.9.2023)<\/a><\/span><\/li>\n<li><span style=\"color: #808080\"><a style=\"color: #808080\" href=\"https:\/\/users.utu.fi\/jkari\/wp-content\/uploads\/sites\/1251\/2023\/09\/homework5.pdf\"><strong>Homework 5<\/strong> (2.10.2023)<\/a><\/span><\/li>\n<li><span style=\"color: #808080\"><a style=\"color: #808080\" href=\"https:\/\/users.utu.fi\/jkari\/wp-content\/uploads\/sites\/1251\/2023\/09\/homework6.pdf\"><strong>Homework 6<\/strong> (5.10.2023)<\/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\/2023\/10\/homework7.pdf\">Homework 7<\/a><\/strong><a style=\"color: #808080\" href=\"https:\/\/users.utu.fi\/jkari\/wp-content\/uploads\/sites\/1251\/2023\/10\/homework7.pdf\"> (9.10.2023)<\/a><\/span><\/li>\n<li><span style=\"color: #808080\"><a style=\"color: #808080\" href=\"https:\/\/users.utu.fi\/jkari\/wp-content\/uploads\/sites\/1251\/2023\/10\/homework8.pdf\"><strong>Homework 8<\/strong> (23.10.2023)<\/a><\/span><\/li>\n<li><span style=\"color: #808080\"><a style=\"color: #808080\" href=\"https:\/\/users.utu.fi\/jkari\/wp-content\/uploads\/sites\/1251\/2023\/10\/homework9.pdf\"><strong>Homework 9<\/strong> (30.10.2023)<\/a><\/span><\/li>\n<li><span style=\"color: #808080\"><a style=\"color: #808080\" href=\"https:\/\/users.utu.fi\/jkari\/wp-content\/uploads\/sites\/1251\/2023\/10\/homework10.pdf\"><strong>Homework 10<\/strong> (6.11.2023)<\/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\/2023\/11\/homework11.pdf\">Homework 11<\/a><\/strong><a style=\"color: #808080\" href=\"https:\/\/users.utu.fi\/jkari\/wp-content\/uploads\/sites\/1251\/2023\/11\/homework11.pdf\"> (13.11.2023)<\/a><\/span><\/li>\n<li><span style=\"color: #808080\"><a style=\"color: #808080\" href=\"https:\/\/users.utu.fi\/jkari\/wp-content\/uploads\/sites\/1251\/2023\/11\/homework12.pdf\"><strong>Homework 12<\/strong> (27.11.2023)<\/a><\/span><\/li>\n<li><strong><span style=\"color: #808080\"><a style=\"color: #808080\" href=\"https:\/\/users.utu.fi\/jkari\/wp-content\/uploads\/sites\/1251\/2023\/11\/homework13.pdf\">Homework 13 <\/a><\/span><\/strong><span style=\"color: #808080\"><a style=\"color: #808080\" href=\"https:\/\/users.utu.fi\/jkari\/wp-content\/uploads\/sites\/1251\/2023\/11\/homework13.pdf\">(4.12.2023)<\/a><\/span><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Fall term 2023 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 Flow chart to determine wall paper groups Robinson&#8217;s aperiodic Wang tile&hellip; <a class=\"more-link\" href=\"https:\/\/users.utu.fi\/jkari\/tilings2023\/\">Continue reading <span class=\"screen-reader-text\">Tilings and Patterns 2023<\/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-493","page","type-page","status-publish","hentry","entry"],"_links":{"self":[{"href":"https:\/\/users.utu.fi\/jkari\/wp-json\/wp\/v2\/pages\/493","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=493"}],"version-history":[{"count":66,"href":"https:\/\/users.utu.fi\/jkari\/wp-json\/wp\/v2\/pages\/493\/revisions"}],"predecessor-version":[{"id":924,"href":"https:\/\/users.utu.fi\/jkari\/wp-json\/wp\/v2\/pages\/493\/revisions\/924"}],"wp:attachment":[{"href":"https:\/\/users.utu.fi\/jkari\/wp-json\/wp\/v2\/media?parent=493"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}