{"version":"1.0","type":"rich","title":"Aperiodic Hat Transformations \ud83c\udfa9","description":"Am I doing this right?\r\n\r\nIn https:\/\/turtletoy.net\/turtle\/61a52c764a the 'Hat' tile is used in a tessellation. Using different ratios for the length of the edges an infinite amount of different shapes are possible for this tessellation (https:\/\/youtu.be\/W-ECvtIA-5A).\r\n\r\nUse the slide for t_morph to 'scroll' through these possibilities. It is a scalar from 0 to 6 (instead of 0 to 1) because there are 6 intervals between the 7 predefined criteria (see lines 56 to 67). The 'hat' is on the 1\/3 interval which cannot be expressed with a slider from 0 to 1. With values from 0 to 6 the 'hat' is at value 2.\r\n\r\nUsing the shoelace approach I solved the problem to keep the area's of the different tile variations the same (lines 86 to 94). However I yet failed to integrate these variations in https:\/\/turtletoy.net\/turtle\/61a52c764a (see https:\/\/turtletoy.net\/turtle\/3fe7611517) because some transformations are applied to polygons that I do not yet fully understand.\r\n\r\nhttps:\/\/cs.uwaterloo.ca\/~csk\/hat\/\r\nhttps:\/\/arxiv.org\/pdf\/2303.10798.pdf","author_name":"Jurgen","author_url":"https:\/\/turtletoy.net\/user\/Jurgen","provider_name":"Turtletoy","provider_url":"https:\/\/turtletoy.net\/","license":{"fullName":"Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International","shortName":"CC BY-NC-SA 4.0","url":"https:\/\/creativecommons.org\/licenses\/by-nc-sa\/4.0\/"},"thumbnail_url":"https:\/\/turtletoy.net\/thumbnail\/a12c818ea0.jpg","thumbnail_width":512,"thumbnail_height":512,"html":"<iframe src=\"https:\/\/turtletoy.net\/embed\/a12c818ea0\" width=\"1025px\" height=\"554px\" style=\"max-width: 100%; border: 0\" sandbox=\"allow-scripts allow-top-navigation allow-top-navigation-by-user-activation allow-forms allow-popups allow-same-origin\"><\/iframe>","width":1025,"height":554}