7.356 DEGREES Copyright 2023 mrkswcz All rights reserved Start with something simple. Take four identical equilateral triangles and join them to form a pyramid. This is your building block – a regular tetrahedron, the simplest possible three-dimensional figure. When you connect five such pyramids by attaching their faces, you will be left with a thin empty space between the first and last: a volumetric angle of 7.356 degrees. It’s too small to fit another piece and too big to be lost in numerical imprecision. It is a surprising imperfection. You would expect a tetrahedron to behave similarly to its two-dimensional ancestor. When you arrange equilateral triangles, one next to the other like tiles, you can cover two-dimensional space without leaving an empty spot. You may go on forever, covering infinite planes and be sure that the six angles that meet at each point will add up to the perfect 360 degrees. In three dimensions, it is not like this: you cannot use your building block to fully fill a void. It’s as if the mathematical rules –the ones we tend to idealise for elegance, harmony, and infallibility– broke when you raise complexity. But mathematical beauty does not reside in perfection. It is through these exceptions that complexity emerges. So keep building, face by face, one block at a time, and embrace the surprising, chaotic aesthetics that appears. A different type of harmony – not based on impeccable proportions, but on unpredictability. ----------------------------- The colors of the structures are inspired by 16 paintings of Polish artists from the 19th and 20th century. "In a window" by Anna Bilinska-Bohdanowicz "Portrait of Jadwiga against a Yellow Background" by Jozef Mehoffer "Portrait of Zofia Okun" by Edward Okun "Girl with chrysanthemums" by Olga Boznanska "Nocturne – Swans in Ogrod Saski in Warsaw by Night" by Jozef Pankiewicz "Soil" by Ferdynand Ruszczyc "Obsession" by Wojciech Weiss "Self-portrait in armor" by Jacek Malczewski "Self-portrait" by Artur Grottger "Portrait of Jadwiga Dembowska" by Leopold Horowitz "Death of Barbara Radziwill" by Jozef Simmler "Before the Sunrise" by Jozef Chelmonski "With brushwood" by Julian Falat Study for the Painting "In a Bower" by Aleksander Gierymski "Woman Combing her Hair" by Wladyslaw Slewinski "Still life with a heron" by Wladyslaw Czachorski ----------------------------- Click on the image for resolution options. In live mode: Click PNG to save the rendered image. [Saving higher resolutions may not work in some browsers; in these cases, right-click-save the image] Click STL or PLY to download the digital model to view on your computer or 3d print at home [experimental]. The PLY format stores colours of the model that can be visualised in most 3d modelling programs. The project uses CPU for calculations and rendering. Generating the image requires up to 500MB of free RAM. Testing was performed across browsers and devices, but please ensure it works on your device before minting. ----------------------------- All drawing and geometric methods are written by mrkswcz using javascript, except for the following: three.js https://threejs.org/ https://github.com/mrdoob/three.js/ The MIT License Copyright © 2010-2022 three.js authors Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the 'Software'), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions: The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software. THE SOFTWARE IS PROVIDED 'AS IS', WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. ----------------------------- three-mesh-bvh https://github.com/gkjohnson/three-mesh-bvh#readme MIT License Copyright (c) 2018 Garrett Johnson Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the 'Software'), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions: The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software. THE SOFTWARE IS PROVIDED 'AS IS', WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. ----------------------------------- seedrandom https://github.com/davidbau/seedrandom Copyright 2019 David Bau. Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the 'Software'), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions: The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software. THE SOFTWARE IS PROVIDED 'AS IS', WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. ----------------------------------- OpenSimplex Noise https://github.com/joshforisha/open-simplex-noise-js Josh Forisha This is free and unencumbered software released into the public domain. Anyone is free to copy, modify, publish, use, compile, sell, or distribute this software, either in source code form or as a compiled binary, for any purpose, commercial or non-commercial, and by any means. In jurisdictions that recognize copyright laws, the author or authors of this software dedicate any and all copyright interest in the software to the public domain. We make this dedication for the benefit of the public at large and to the detriment of our heirs and successors. We intend this dedication to be an overt act of relinquishment in perpetuity of all present and future rights to this software under copyright law. THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. For more information, please refer to ----------------------------------- triangle-triangle-intersection https://github.com/stonkpunk/my-npm-modules/tree/main/triangle-triangle-intersection by stonkpunk based on http://web.stanford.edu/class/cs277/resources/papers/Moller1997b.pdf CC0 1.0 Universal (CC0 1.0) Public Domain Dedication No Copyright The person who associated a work with this deed has dedicated the work to the public domain by waiving all of his or her rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission. See Other Information below. Other Information - In no way are the patent or trademark rights of any person affected by CC0, nor are the rights that other persons may have in the work or in how the work is used, such as publicity or privacy rights. - Unless expressly stated otherwise, the person who associated a work with this deed makes no warranties about the work, and disclaims liability for all uses of the work, to the fullest extent permitted by applicable law. - When using or citing the work, you should not imply endorsement by the author or the affirmer. ----------------------------------- Compiled using fxhash-boilerplate-webpack by fxhash under MIT License Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the 'Software'), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions: The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software. THE SOFTWARE IS PROVIDED 'AS IS', WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.