{"id":5222,"date":"2018-12-29T16:22:22","date_gmt":"2018-12-29T23:22:22","guid":{"rendered":"http:\/\/theoryofeverything.org\/theToE\/?p=5222"},"modified":"2018-12-31T11:36:10","modified_gmt":"2018-12-31T18:36:10","slug":"integer-compositions-gray-code-and-the-fibonacci-sequence","status":"publish","type":"post","link":"https:\/\/theoryofeverything.org\/theToE\/2018\/12\/29\/integer-compositions-gray-code-and-the-fibonacci-sequence\/","title":{"rendered":"Integer Compositions, Gray Code , and the Fibonacci Sequence"},"content":{"rendered":"<p>I was prompted by Chris Birke to take a look at <a href=\"https:\/\/digitalcommons.georgiasouthern.edu\/cgi\/viewcontent.cgi?article=1012&amp;context=etd\">this very interesting paper<\/a> by Linus Lindroos. Chris is working with my E8 to H4 Folding Matrix for optimizing computation using network theory and hyper-dimensional geometric structures.<\/p>\n<p>I was able to validate the paper with some quick Mathematica code.<\/p>\n<p>Below is the code that sets up the generation of the tables, including various binary, numeric, and symbolic (graph) Compositions.<br \/>\n<a href=\"http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2018\/12\/Fibbinary-Gray-Compositions.png\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-5224\" src=\"http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2018\/12\/Fibbinary-Gray-Compositions.png\" alt=\"\" width=\"829\" height=\"2102\" srcset=\"https:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2018\/12\/Fibbinary-Gray-Compositions.png 829w, https:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2018\/12\/Fibbinary-Gray-Compositions-197x500.png 197w, https:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2018\/12\/Fibbinary-Gray-Compositions-404x1024.png 404w\" sizes=\"auto, (max-width: 829px) 100vw, 829px\" \/><\/a><\/p>\n<p>Notice the last statement (above) lists the odd FibBinaries (up to N=200) as related to the Floor of the n*Phi^2-1, with n=1 to 77.<\/p>\n<p>Below is a listing of the first 100 N integers represented by their odd and even FibBinaries, along with the binary and Gray code Compositions.<br \/>\n<a href=\"http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2018\/12\/Odd-Even-Fibinnaries-1.png\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2018\/12\/Odd-Even-Fibinnaries-1.png\" alt=\"\" width=\"796\" height=\"2192\" class=\"aligncenter size-full wp-image-5228\" srcset=\"https:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2018\/12\/Odd-Even-Fibinnaries-1.png 796w, https:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2018\/12\/Odd-Even-Fibinnaries-1-182x500.png 182w, https:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2018\/12\/Odd-Even-Fibinnaries-1-372x1024.png 372w\" sizes=\"auto, (max-width: 796px) 100vw, 796px\" \/><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>I was prompted by Chris Birke to take a look at this very interesting paper by Linus Lindroos. Chris is working with my E8 to H4 Folding Matrix for optimizing computation using network theory and hyper-dimensional geometric structures. I was able to validate the paper with some quick Mathematica code. Below is the code that &hellip; <a href=\"https:\/\/theoryofeverything.org\/theToE\/2018\/12\/29\/integer-compositions-gray-code-and-the-fibonacci-sequence\/\" class=\"more-link\">Continue reading <span class=\"screen-reader-text\">Integer Compositions, Gray Code , and the Fibonacci Sequence<\/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":[14],"class_list":["post-5222","post","type-post","status-publish","format-standard","hentry","category-physics","tag-math"],"aioseo_notices":[],"aioseo_head":"\n\t\t<!-- All in One SEO 4.9.10 - aioseo.com -->\n\t<meta name=\"description\" content=\"I was prompted by Chris Birke to take a look at this very interesting paper by Linus Lindroos. Chris is working with my E8 to H4 Folding Matrix for optimizing computation using network theory and hyper-dimensional geometric structures. I was able to validate the paper with some quick Mathematica code. 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Chris is working with my E8 to H4 Folding Matrix for optimizing computation using network theory and hyper-dimensional geometric structures. I was able to validate the paper with some quick Mathematica code. Below is the code that\" \/>\n\t\t<meta property=\"og:url\" content=\"https:\/\/theoryofeverything.org\/theToE\/2018\/12\/29\/integer-compositions-gray-code-and-the-fibonacci-sequence\/\" \/>\n\t\t<meta property=\"article:published_time\" content=\"2018-12-29T23:22:22+00:00\" \/>\n\t\t<meta property=\"article:modified_time\" content=\"2018-12-31T18:36:10+00:00\" \/>\n\t\t<meta name=\"twitter:card\" content=\"summary\" \/>\n\t\t<meta name=\"twitter:title\" content=\"Integer Compositions, Gray Code , and the Fibonacci Sequence - Visualizing a Theory of Everything!\" \/>\n\t\t<meta name=\"twitter:description\" content=\"I was prompted by Chris Birke to take a look at this very interesting paper by Linus Lindroos. Chris is working with my E8 to H4 Folding Matrix for optimizing computation using network theory and hyper-dimensional geometric structures. I was able to validate the paper with some quick Mathematica code. Below is the code that\" \/>\n\t\t<script type=\"application\/ld+json\" class=\"aioseo-schema\">\n\t\t\t{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"BlogPosting\",\"@id\":\"https:\\\/\\\/theoryofeverything.org\\\/theToE\\\/2018\\\/12\\\/29\\\/integer-compositions-gray-code-and-the-fibonacci-sequence\\\/#blogposting\",\"name\":\"Integer Compositions, Gray Code , and the Fibonacci Sequence - Visualizing a Theory of Everything!\",\"headline\":\"Integer Compositions, Gray Code , and the Fibonacci Sequence\",\"author\":{\"@id\":\"https:\\\/\\\/theoryofeverything.org\\\/theToE\\\/author\\\/jgmoxness\\\/#author\"},\"publisher\":{\"@id\":\"https:\\\/\\\/theoryofeverything.org\\\/theToE\\\/#person\"},\"image\":{\"@type\":\"ImageObject\",\"url\":\"https:\\\/\\\/theoryofeverything.org\\\/theToE\\\/wp-content\\\/uploads\\\/2018\\\/12\\\/Fibbinary-Gray-Compositions.png\",\"@id\":\"https:\\\/\\\/theoryofeverything.org\\\/theToE\\\/2018\\\/12\\\/29\\\/integer-compositions-gray-code-and-the-fibonacci-sequence\\\/#articleImage\",\"width\":829,\"height\":2102},\"datePublished\":\"2018-12-29T16:22:22-07:00\",\"dateModified\":\"2018-12-31T11:36:10-07:00\",\"inLanguage\":\"en-US\",\"mainEntityOfPage\":{\"@id\":\"https:\\\/\\\/theoryofeverything.org\\\/theToE\\\/2018\\\/12\\\/29\\\/integer-compositions-gray-code-and-the-fibonacci-sequence\\\/#webpage\"},\"isPartOf\":{\"@id\":\"https:\\\/\\\/theoryofeverything.org\\\/theToE\\\/2018\\\/12\\\/29\\\/integer-compositions-gray-code-and-the-fibonacci-sequence\\\/#webpage\"},\"articleSection\":\"Physics, Math\"},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\\\/\\\/theoryofeverything.org\\\/theToE\\\/2018\\\/12\\\/29\\\/integer-compositions-gray-code-and-the-fibonacci-sequence\\\/#breadcrumblist\",\"itemListElement\":[{\"@type\":\"ListItem\",\"@id\":\"https:\\\/\\\/theoryofeverything.org\\\/theToE#listItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\\\/\\\/theoryofeverything.org\\\/theToE\",\"nextItem\":{\"@type\":\"ListItem\",\"@id\":\"https:\\\/\\\/theoryofeverything.org\\\/theToE\\\/topics\\\/physics\\\/#listItem\",\"name\":\"Physics\"}},{\"@type\":\"ListItem\",\"@id\":\"https:\\\/\\\/theoryofeverything.org\\\/theToE\\\/topics\\\/physics\\\/#listItem\",\"position\":2,\"name\":\"Physics\",\"item\":\"https:\\\/\\\/theoryofeverything.org\\\/theToE\\\/topics\\\/physics\\\/\",\"nextItem\":{\"@type\":\"ListItem\",\"@id\":\"https:\\\/\\\/theoryofeverything.org\\\/theToE\\\/2018\\\/12\\\/29\\\/integer-compositions-gray-code-and-the-fibonacci-sequence\\\/#listItem\",\"name\":\"Integer Compositions, Gray Code , and the Fibonacci Sequence\"},\"previousItem\":{\"@type\":\"ListItem\",\"@id\":\"https:\\\/\\\/theoryofeverything.org\\\/theToE#listItem\",\"name\":\"Home\"}},{\"@type\":\"ListItem\",\"@id\":\"https:\\\/\\\/theoryofeverything.org\\\/theToE\\\/2018\\\/12\\\/29\\\/integer-compositions-gray-code-and-the-fibonacci-sequence\\\/#listItem\",\"position\":3,\"name\":\"Integer Compositions, Gray Code , and the Fibonacci Sequence\",\"previousItem\":{\"@type\":\"ListItem\",\"@id\":\"https:\\\/\\\/theoryofeverything.org\\\/theToE\\\/topics\\\/physics\\\/#listItem\",\"name\":\"Physics\"}}]},{\"@type\":\"Person\",\"@id\":\"https:\\\/\\\/theoryofeverything.org\\\/theToE\\\/#person\",\"name\":\"jgmoxness\"},{\"@type\":\"Person\",\"@id\":\"https:\\\/\\\/theoryofeverything.org\\\/theToE\\\/author\\\/jgmoxness\\\/#author\",\"url\":\"https:\\\/\\\/theoryofeverything.org\\\/theToE\\\/author\\\/jgmoxness\\\/\",\"name\":\"jgmoxness\"},{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/theoryofeverything.org\\\/theToE\\\/2018\\\/12\\\/29\\\/integer-compositions-gray-code-and-the-fibonacci-sequence\\\/#webpage\",\"url\":\"https:\\\/\\\/theoryofeverything.org\\\/theToE\\\/2018\\\/12\\\/29\\\/integer-compositions-gray-code-and-the-fibonacci-sequence\\\/\",\"name\":\"Integer Compositions, Gray Code , and the Fibonacci Sequence - Visualizing a Theory of Everything!\",\"description\":\"I was prompted by Chris Birke to take a look at this very interesting paper by Linus Lindroos. 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Below is the code that"},"aioseo_meta_data":{"post_id":"5222","title":null,"description":null,"keywords":null,"keyphrases":null,"primary_term":null,"canonical_url":null,"og_title":null,"og_description":null,"og_object_type":"default","og_image_type":"default","og_image_url":null,"og_image_width":null,"og_image_height":null,"og_image_custom_url":null,"og_image_custom_fields":null,"og_video":null,"og_custom_url":null,"og_article_section":null,"og_article_tags":null,"twitter_use_og":false,"twitter_card":"default","twitter_image_type":"default","twitter_image_url":null,"twitter_image_custom_url":null,"twitter_image_custom_fields":null,"twitter_title":null,"twitter_description":null,"schema":{"blockGraphs":[],"customGraphs":[],"default":{"data":{"Article":[],"Course":[],"Dataset":[],"FAQPage":[],"Movie":[],"Person":[],"Product":[],"ProductReview":[],"Car":[],"Recipe":[],"Service":[],"SoftwareApplication":[],"WebPage":[]},"graphName":"","isEnabled":true},"graphs":[]},"schema_type":"default","schema_type_options":null,"pillar_content":false,"robots_default":true,"robots_noindex":false,"robots_noarchive":false,"robots_nosnippet":false,"robots_nofollow":false,"robots_noimageindex":false,"robots_noodp":false,"robots_notranslate":false,"robots_max_snippet":null,"robots_max_videopreview":null,"robots_max_imagepreview":"large","priority":null,"frequency":null,"local_seo":null,"limit_modified_date":false,"created":"2022-04-06 04:26:00","updated":"2025-06-10 15:51:18"},"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\tInteger Compositions, Gray Code , and the Fibonacci Sequence\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":"Integer Compositions, Gray Code , and the Fibonacci Sequence","link":"https:\/\/theoryofeverything.org\/theToE\/2018\/12\/29\/integer-compositions-gray-code-and-the-fibonacci-sequence\/"}],"_links":{"self":[{"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/posts\/5222","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/comments?post=5222"}],"version-history":[{"count":5,"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/posts\/5222\/revisions"}],"predecessor-version":[{"id":5234,"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/posts\/5222\/revisions\/5234"}],"wp:attachment":[{"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/media?parent=5222"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/categories?post=5222"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/tags?post=5222"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}