{"id":8101,"date":"2026-06-26T15:33:55","date_gmt":"2026-06-26T22:33:55","guid":{"rendered":"https:\/\/theoryofeverything.org\/theToE\/?p=8101"},"modified":"2026-07-14T09:37:10","modified_gmt":"2026-07-14T16:37:10","slug":"e8-and-h4-hopf-fibrations-with-the-aizawa-chaotic-attractor","status":"publish","type":"post","link":"http:\/\/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

If you are working with topological field theoretic 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 all of these concepts visually!<\/p>\n\n\n\n

Click on the PNG image to get the SVG version.<\/p>\n\n\n

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E8 Hopf Fibration<\/figcaption><\/figure>\n<\/div>\n\n
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H4 600-cell Hopf Fibration<\/figcaption><\/figure>\n<\/div>\n\n
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The H4 120-cell Hopf Fibration<\/figcaption><\/figure>\n<\/div>\n\n
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The Aizawa Chaotic Attractor<\/figcaption><\/figure>\n<\/div>\n\n\n

This is all also related to the Clifford algebra of Cl(9,0) with the Bott Periodicity clock showing the related algebras (click for SVG):<\/p>\n\n\n

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Bott Periodicity Clock of Cl(9,0) as it relates to the Hopf Fibration of CP4<\/sup><\/figcaption><\/figure>\n<\/div>\n\n\n

The Bott periodicity clock uses a Mod 8 clock face with second hand mnemonics taken from the I-Ching with the real Clifford algebra of signature (p,q) denoted as Clp,q<\/sub>(R)=Cl(p,q). An animated (GIF) example is on the Bott Periodicity Wikipedia page<\/a>.<\/p>\n\n\n\n

A few more geometries:<\/p>\n\n\n

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The envelope of the vertex first 600-cell aka. PentakisIcosidodecahedron<\/figcaption><\/figure>\n<\/div>\n\n
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The envelope of the cell first 120-cell aka. Chamferred Dodecahedron<\/figcaption><\/figure>\n<\/div>\n\n
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The Icosahedron @ quality 3<\/figcaption><\/figure>\n<\/div>\n\n\n

<\/p>\n","protected":false},"excerpt":{"rendered":"

If you are working with topological field theoretic 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 all of … Continue reading E8 and H4 Hopf Fibrations with the Aizawa Chaotic Attractor<\/span> →<\/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\n\t\n\t\n\t\n\t\n\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t