{"id":8101,"date":"2026-06-26T15:33:55","date_gmt":"2026-06-26T22:33:55","guid":{"rendered":"https:\/\/theoryofeverything.org\/theToE\/?p=8101"},"modified":"2026-06-26T17:16:04","modified_gmt":"2026-06-27T00:16:04","slug":"e8-and-h4-hopf-fibrations-with-the-aizawa-chaotic-attractor","status":"publish","type":"post","link":"https:\/\/theoryofeverything.org\/theToE\/2026\/06\/26\/e8-and-h4-hopf-fibrations-with-the-aizawa-chaotic-attractor\/","title":{"rendered":"E8 and H4 Hopf Fibrations with the Aizawa Chaotic Attractor"},"content":{"rendered":"\n<p>If you are working with topological field theory Hopf fibrations, chaotic attractors, and\/or E8 and any of its extensive set of maximal subgroups, polytopes, lattices and codes or its folded (rotated) H4 family of polytopes (e.g. 600 and 120 cells in their vertex, cell, face, and edge orientations), VisibLie_E8 can group theoretically integrate these concepts visually!<\/p>\n\n\n\n<p>Click on the PNG image to get the SVG version.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><a href=\"https:\/\/theoryofeverything.org\/TOE\/JGM\/outChaos_E8.svg\" target=\"_blank\" rel=\" noreferrer noopener\"><img decoding=\"async\" src=\"https:\/\/theoryofeverything.org\/TOE\/JGM\/outChaos_E8.png\" alt=\"\"\/><\/a><figcaption class=\"wp-element-caption\">E8 Hopf Fibration<\/figcaption><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><a href=\"https:\/\/theoryofeverything.org\/TOE\/JGM\/outChaos_600cell_E8.svg\" target=\"_blank\" rel=\" noreferrer noopener\"><img decoding=\"async\" src=\"https:\/\/theoryofeverything.org\/TOE\/JGM\/outChaos_600cell_E8.png\" alt=\"\"\/><\/a><figcaption class=\"wp-element-caption\">H4 600-cell Hopf Fibration<\/figcaption><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><a href=\"https:\/\/theoryofeverything.org\/TOE\/JGM\/outChaos_120cell_E8.svg\" target=\"_blank\" rel=\" noreferrer noopener\"><img decoding=\"async\" src=\"https:\/\/theoryofeverything.org\/TOE\/JGM\/outChaos_120cell_E8.png\" alt=\"\"\/><\/a><figcaption class=\"wp-element-caption\">The H4 120-cell Hopf Fibration<\/figcaption><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"973\" height=\"750\" src=\"http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2026\/06\/Aizawa-Chaotic-Attractor.png\" alt=\"\" class=\"wp-image-8102\"\/><figcaption class=\"wp-element-caption\">The Aizawa Chaotic Attractor<\/figcaption><\/figure>\n<\/div>\n\n\n<p>A few more geometries:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><a href=\"https:\/\/theoryofeverything.org\/TOE\/JGM\/outChaos_PentakisIcosidodecahedron.svg\" target=\"_blank\" rel=\" noreferrer noopener\"><img decoding=\"async\" src=\"https:\/\/theoryofeverything.org\/TOE\/JGM\/outChaos_PentakisIcosidodecahedron.png\" alt=\"\"\/><\/a><figcaption class=\"wp-element-caption\">The envelope of the vertex first 600-cell aka. PentakisIcosidodecahedron<\/figcaption><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><a href=\"https:\/\/theoryofeverything.org\/TOE\/JGM\/outChaos_Icosahedron.svg\" target=\"_blank\" rel=\" noreferrer noopener\"><img decoding=\"async\" src=\"https:\/\/theoryofeverything.org\/TOE\/JGM\/outChaos_Icosahedron.png\" alt=\"\"\/><\/a><figcaption class=\"wp-element-caption\">The envelope of the cell first 120-cell aka. Chamferred Dodecahedron<\/figcaption><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><a href=\"https:\/\/theoryofeverything.org\/TOE\/JGM\/outChaos_Icosahedron.svg\" target=\"_blank\" rel=\" noreferrer noopener\"><img decoding=\"async\" src=\"https:\/\/theoryofeverything.org\/TOE\/JGM\/outChaos_Icosahedron.png\" alt=\"\"\/><\/a><figcaption class=\"wp-element-caption\">The Icosahedron @ quality 3<\/figcaption><\/figure>\n<\/div>\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>If you are working with topological field theory Hopf fibrations, chaotic attractors, and\/or E8 and any of its extensive set of maximal subgroups, polytopes, lattices and codes or its folded (rotated) H4 family of polytopes (e.g. 600 and 120 cells in their vertex, cell, face, and edge orientations), VisibLie_E8 can group theoretically integrate these concepts &hellip; <a href=\"https:\/\/theoryofeverything.org\/theToE\/2026\/06\/26\/e8-and-h4-hopf-fibrations-with-the-aizawa-chaotic-attractor\/\" class=\"more-link\">Continue reading <span class=\"screen-reader-text\">E8 and H4 Hopf Fibrations with the Aizawa Chaotic Attractor<\/span> <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[30,4,34,58,14,16],"class_list":["post-8101","post","type-post","status-publish","format-standard","hentry","category-physics","tag-chaos","tag-e8","tag-h4","tag-hopf","tag-math","tag-physics"],"aioseo_notices":[],"aioseo_head":"\n\t\t<!-- All in One SEO 4.9.8 - aioseo.com -->\n\t<meta name=\"description\" content=\"If you are working with topological field theory Hopf fibrations, chaotic attractors, and\/or E8 and any of its extensive set of maximal subgroups, polytopes, lattices 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22:01:37","updated":"2026-06-27 00:16:04"},"aioseo_breadcrumb":"<div class=\"aioseo-breadcrumbs\"><span class=\"aioseo-breadcrumb\">\n\t\t\t<a href=\"https:\/\/theoryofeverything.org\/theToE\" title=\"Home\">Home<\/a>\n\t\t<\/span><span class=\"aioseo-breadcrumb-separator\">\u00bb<\/span><span class=\"aioseo-breadcrumb\">\n\t\t\t<a href=\"https:\/\/theoryofeverything.org\/theToE\/topics\/physics\/\" title=\"Physics\">Physics<\/a>\n\t\t<\/span><span class=\"aioseo-breadcrumb-separator\">\u00bb<\/span><span class=\"aioseo-breadcrumb\">\n\t\t\tE8 and H4 Hopf Fibrations with the Aizawa Chaotic Attractor\n\t\t<\/span><\/div>","aioseo_breadcrumb_json":[{"label":"Home","link":"https:\/\/theoryofeverything.org\/theToE"},{"label":"Physics","link":"https:\/\/theoryofeverything.org\/theToE\/topics\/physics\/"},{"label":"E8 and H4 Hopf Fibrations with the Aizawa Chaotic 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