{"id":132,"date":"2016-11-15T22:49:40","date_gmt":"2016-11-15T22:49:40","guid":{"rendered":"http:\/\/jensmeisner.net\/?p=132"},"modified":"2020-05-28T21:45:28","modified_gmt":"2020-05-28T21:45:28","slug":"afteronedotsixoneeight","status":"publish","type":"post","link":"https:\/\/jensmeisner.net\/de\/afteronedotsixoneeight\/","title":{"rendered":"AfterOneDotSixOneEight"},"content":{"rendered":"<p>This visualization software calculates one position of the Fibonacci sequence, and its surrounding neighbors. The division of two neighbors creates a number, also known as Golden Ratio. The y axis represents this calculated numbers of the Golden Ratio according to the Fibonacci sequence, while its decimals behind the comma are shown along the x-axis.<\/p>\n<div style=\"width: 680px;\" class=\"wp-video\"><video class=\"wp-video-shortcode\" id=\"video-132-1\" width=\"680\" height=\"383\" preload=\"auto\" controls=\"controls\"><source type=\"video\/mp4\" src=\"http:\/\/jensmeisner.net\/wp-content\/uploads\/2016\/11\/AfterOneDotSixOneEight.mp4?_=1\" \/><a href=\"http:\/\/jensmeisner.net\/wp-content\/uploads\/2016\/11\/AfterOneDotSixOneEight.mp4\">http:\/\/jensmeisner.net\/wp-content\/uploads\/2016\/11\/AfterOneDotSixOneEight.mp4<\/a><\/video><\/div>\n<p><strong>BACKGROUND<\/strong><\/p>\n<p>The sequence of Fibonacci numbers result from a repeated iteration of a function, in which the output of one iteration is used as an input for the next iteration. In the scientists challenge to answer the question of how does work nature, the actual number sequence can be wittnessed everywhere, e.g. flower petals, seed heads, fruits, vegetables, pine-cones, trees, shells, spiral galaxies, human anatomy, DNA molecules, and even insect flight patterns.<\/p>\n<p>If a Fibonacci number is divided by its immediate predecessor, the quotient approximates phi, or better known as Golden Ratio. A good example of using values from the Fibonacci sequence in geometry is the Golden Spiral.<\/p>\n<p>The history of the Fibonacci sequence and the resulting Golden Ratio goes back to ancient Sanskrit poetry, in which the first numbers of a Fibonacci sequence has been used to create the very rhythmical structure of poems, the meter. Later on, in ancient Greece ca. 300 B.C., Euclid of Alexandria took on this number sequence to implement it into his geometrical approach, calling it \u201cextreme and mean ratio\u201d.<\/p>\n<p>The term De divina proportione, or \u201cDivine proportion\u201d is mentioned first time by Mathematician Luca Pacioli in his work with same name published in 1509. Adding the word \u201cGolden\u201d in 1835 by Mathematician Marin Ohm completed the journey of name creation to the todays known Golden Ratio.<\/p>\n<p>However, the Fibonacci sequence has its name from the Italian Mathematician Leonardo Bonacci, also know as Fibonacci. In his work \u201cLiber Aabci\u201d (Book of Calculation) published 1202, he introduced the sequence to Europe, when he used it as an example to explain the growth of rabbit population based on idealized assumptions. But the Fibonacci number and its related Golden Ratio has not only be used by humans to create an answer to a rabbit problem.<\/p>\n<p><strong>SOFTWARE<\/strong><\/p>\n<p>To realize the approach of visualizing the Fibonacci sequence in its fast growing size on one hand, while calculating the continuous shrinking fractional part described by decimals of the Golden Ration on the other hand, an OpenGL application written in C++ using openFrameworks is one suitable way of accomplishing the task. On the very heart of the program, the Fibonacci sequence is created by a for loop, which adds each new calculated Fibonacci number to the end of a list, also known as dynamic array or vector. This \u201clist\u201d will go through another loop, that takes the predecessor, divides it to get the Golden Ration, especially the decimals of its fractional part. The result gets added to yet another \u201clist\u201d (array), thus building the basis of the visualization.<\/p>\n<p>Each calculated Golden Ratio ends up with a different fractional part, depending on which position of the Fibonacci sequence is used to calculate it. The decimals are then used to dedicate the color and height of cubes used for each decimal in the final visuals.<\/p>\n<p>Decimal to Colors:<\/p>\n<p>0\u2192White : 1\u2192Red : 2\u2192Sienna : 3\u2192Orange : 4\u2192Yellow : 5\u2192Green : 6\u2192Blue : 7\u2192Lilac : 8\u2192Pink : 9\u2192 Black<\/p>\n<p><strong>Graphical User Interface<\/strong><em><br \/>\n<\/em><\/p>\n<p>Control panel:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-156\" src=\"http:\/\/jensmeisner.net\/wp-content\/uploads\/2016\/11\/GUI_1.png\" alt=\"gui_1\" width=\"201\" height=\"238\" \/><\/p>\n<p>FULLSCREEN: Toggles window size to full screen mode<\/p>\n<p>FIBONACCI: Enter a position of the Fibonacci sequence<\/p>\n<p>FRACTION: Enter a position of a decimal in the fractional part of the Golden Ratio<\/p>\n<p>GENERATE: Press button to start calculating the matrix and to generate the visuals<\/p>\n<p>SNAPSHOT: Press button to save an image of the result<\/p>\n<p>TOGGLE Z-VALUE: Add third dimension to the visuals<\/p>\n<p>ORTHO\/PERSP: Switches between orthographic and perspective view<\/p>\n<p>HELP: Displays help section<\/p>\n<p>COLLAPSE CONTROLS: Hides\/Unhides control panel<\/p>\n<ol>\n<li>Add numbers and generate visuals<\/li>\n<\/ol>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-157 size-large\" src=\"http:\/\/jensmeisner.net\/wp-content\/uploads\/2016\/11\/GUI_2-1024x594.png\" alt=\"gui_2\" width=\"620\" height=\"360\" srcset=\"https:\/\/jensmeisner.net\/wp-content\/uploads\/2016\/11\/GUI_2-1024x594.png 1024w, https:\/\/jensmeisner.net\/wp-content\/uploads\/2016\/11\/GUI_2-300x174.png 300w, https:\/\/jensmeisner.net\/wp-content\/uploads\/2016\/11\/GUI_2-768x445.png 768w, https:\/\/jensmeisner.net\/wp-content\/uploads\/2016\/11\/GUI_2.png 1278w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/p>\n<p>An example of a generated Fibonacci position is:<\/p>\n<p><span style=\"color: #e7e7e7;\"><span style=\"color: #000000;\">Fibonacci[2056] is<\/span><\/span><\/p>\n<p><span style=\"color: #e7e7e7;\"><span style=\"color: #000000;\"><br \/>\n131860801595908281373128706367564492853244378329190316353226<\/span><\/span><span style=\"color: #e7e7e7;\"><span style=\"color: #000000;\">139378917209631841347153<\/span><\/span><span style=\"color: #e7e7e7;\"><span style=\"color: #000000;\">69565392153900272<\/span><\/span><\/p>\n<p><span style=\"color: #e7e7e7;\"><span style=\"color: #000000;\">32937421691913960413<\/span><\/span><span style=\"color: #e7e7e7;\"><span style=\"color: #000000;\">3919507709920088316844488855976191856642407848<\/span><\/span><span style=\"color: #e7e7e7;\"><span style=\"color: #000000;\">6328770189526<\/span><\/span><span style=\"color: #e7e7e7;\"><span style=\"color: #000000;\">1102339916959964553619<\/span><\/span><\/p>\n<p><span style=\"color: #e7e7e7;\"><span style=\"color: #000000;\">187257531373044974231606285462757981706<\/span><\/span><span style=\"color: #e7e7e7;\"><span style=\"color: #000000;\">32474563951<\/span><\/span><span style=\"color: #e7e7e7;\"><span style=\"color: #000000;\">6366960226764939459189642866338813633719859496522<\/span><\/span><span style=\"color: #e7e7e7;\"><span style=\"color: #000000;\">63<\/span><\/span><\/p>\n<p><span style=\"color: #e7e7e7;\"><span style=\"color: #000000;\">39578224614966524164672910284268<\/span><\/span><span style=\"color: #e7e7e7;\"><span style=\"color: #000000;\">55974063267554503559819309885147303740836925226711064953420823167859<\/span><\/span><\/p>\n<p><span style=\"color: #e7e7e7;\"><span style=\"color: #000000;\">775147772048560<\/span><\/span><span style=\"color: #e7e7e7;\"><span style=\"color: #000000;\">71395313570<\/span><\/span><\/p>\n<ol start=\"2\">\n<li>Toggle Z-value<\/li>\n<\/ol>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-158 size-large\" src=\"http:\/\/jensmeisner.net\/wp-content\/uploads\/2016\/11\/GUI_3-1024x594.png\" alt=\"gui_3\" width=\"620\" height=\"360\" srcset=\"https:\/\/jensmeisner.net\/wp-content\/uploads\/2016\/11\/GUI_3-1024x594.png 1024w, https:\/\/jensmeisner.net\/wp-content\/uploads\/2016\/11\/GUI_3-300x174.png 300w, https:\/\/jensmeisner.net\/wp-content\/uploads\/2016\/11\/GUI_3-768x445.png 768w, https:\/\/jensmeisner.net\/wp-content\/uploads\/2016\/11\/GUI_3.png 1280w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/p>\n<ol start=\"3\">\n<li>Find the accuracy line of the Golden Ratio: The higher the number in the Fibonacci sequence, the more accurate the result of the Golden Ratio in its fractional part.<\/li>\n<\/ol>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-159 size-large\" src=\"http:\/\/jensmeisner.net\/wp-content\/uploads\/2016\/11\/GUI_4-1024x595.png\" alt=\"gui_4\" width=\"620\" height=\"360\" srcset=\"https:\/\/jensmeisner.net\/wp-content\/uploads\/2016\/11\/GUI_4-1024x595.png 1024w, https:\/\/jensmeisner.net\/wp-content\/uploads\/2016\/11\/GUI_4-300x174.png 300w, https:\/\/jensmeisner.net\/wp-content\/uploads\/2016\/11\/GUI_4-768x446.png 768w, https:\/\/jensmeisner.net\/wp-content\/uploads\/2016\/11\/GUI_4.png 1280w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/p>\n<p><a href=\"https:\/\/github.com\/iShapeNoise\/AfterOneDotSixOneEight.git\">SOURCE CODE on Github<\/a><\/p>\n<p><b>_<strong><strong>__<\/strong><\/strong><\/b><b><strong><strong><strong><strong><strong><strong><strong><strong>____<\/strong><\/strong><\/strong><\/strong><\/strong><\/strong><\/strong><\/strong><\/b><\/p>\n<p><b>EXHIBIT 2016<\/b><\/p>\n<p>For the exhibition &quot;METASIS&quot; in 2016, the 2016th position of the Fibonacci sequence -&gt;<\/p>\n<p>13186080159590828137312870636756449285324437832919031635322613937891720963184134715369565392153900272<\/p>\n<p>32937421691913960413391950770992008831684448885597619185664240784863287701895261102339916959964553619<\/p>\n<p>18725753137304497423160628546275798170632474563951636696022676493945918964286633881363371985949652263<\/p>\n<p>3957822461496652416467291028426855974063267554503559819309885147303740836925226711064953420823167859<\/p>\n<p>77514777204856071395313570<\/p>\n<p>The number as implementation for the Golden Ration represented as middle row, generated following visuals<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-140 size-large alignleft\" src=\"http:\/\/jensmeisner.net\/wp-content\/uploads\/2016\/11\/afteronedotsixoneeight_2016-1024x231.png\" alt=\"afteronedotsixoneeight_2016\" width=\"620\" height=\"140\" srcset=\"https:\/\/jensmeisner.net\/wp-content\/uploads\/2016\/11\/afteronedotsixoneeight_2016-1024x231.png 1024w, https:\/\/jensmeisner.net\/wp-content\/uploads\/2016\/11\/afteronedotsixoneeight_2016-300x68.png 300w, https:\/\/jensmeisner.net\/wp-content\/uploads\/2016\/11\/afteronedotsixoneeight_2016-768x173.png 768w, https:\/\/jensmeisner.net\/wp-content\/uploads\/2016\/11\/afteronedotsixoneeight_2016.png 1110w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/p>\n<p>This has been used as draft to produce a representation made with wood and acrylic paint.<\/p>\n<p>&quot;AfterOneDotSixOneEight&quot; 240 x 60 cm<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignleft wp-image-141 size-large\" src=\"http:\/\/jensmeisner.net\/wp-content\/uploads\/2016\/11\/Exhibit_AfterOneDotSixOneEight-1024x272.jpg\" alt=\"exhibit_afteronedotsixoneeight\" width=\"620\" height=\"165\" srcset=\"https:\/\/jensmeisner.net\/wp-content\/uploads\/2016\/11\/Exhibit_AfterOneDotSixOneEight-1024x272.jpg 1024w, https:\/\/jensmeisner.net\/wp-content\/uploads\/2016\/11\/Exhibit_AfterOneDotSixOneEight-300x80.jpg 300w, https:\/\/jensmeisner.net\/wp-content\/uploads\/2016\/11\/Exhibit_AfterOneDotSixOneEight-768x204.jpg 768w, https:\/\/jensmeisner.net\/wp-content\/uploads\/2016\/11\/Exhibit_AfterOneDotSixOneEight.jpg 1818w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/p>\n<hr \/>\n<p><b>EXHIBIT 2017<\/b><\/p>\n<p>In this version I decided to use the 129064th position of the Fibonacci sequence, which has 26973 digits -&gt;<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-313 size-full alignnone\" src=\"http:\/\/jensmeisner.net\/wp-content\/uploads\/2016\/11\/fibo129064.png\" alt=\"\" width=\"600\" height=\"5261\" \/><\/p>\n<p>Software-generated draft, that uses fibonacci number above to calculate Golden Ratio,<\/p>\n<p>which is represented as middle row of this piece. The line between repitition and noise<\/p>\n<p>goes along the 53888th digit behind 1.618:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-306 size-large alignnone\" src=\"http:\/\/jensmeisner.net\/wp-content\/uploads\/2016\/11\/AfterOneDotSixOneEight_Draft_Ver2_129024_53888-1024x263.png\" alt=\"\" width=\"620\" height=\"159\" srcset=\"https:\/\/jensmeisner.net\/wp-content\/uploads\/2016\/11\/AfterOneDotSixOneEight_Draft_Ver2_129024_53888-1024x263.png 1024w, https:\/\/jensmeisner.net\/wp-content\/uploads\/2016\/11\/AfterOneDotSixOneEight_Draft_Ver2_129024_53888-300x77.png 300w, https:\/\/jensmeisner.net\/wp-content\/uploads\/2016\/11\/AfterOneDotSixOneEight_Draft_Ver2_129024_53888-768x197.png 768w, https:\/\/jensmeisner.net\/wp-content\/uploads\/2016\/11\/AfterOneDotSixOneEight_Draft_Ver2_129024_53888.png 1991w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/p>\n<p>The final piece is made of canvas, metal fence mesh and acrylic paint. It is made of 3 canvas<\/p>\n<p>in size 90x60 cm.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-large wp-image-307\" src=\"http:\/\/jensmeisner.net\/wp-content\/uploads\/2016\/11\/AfterOneDotSixOneEight_Exhibit_Ver2_129024_53888-1024x322.jpg\" alt=\"\" width=\"620\" height=\"195\" srcset=\"https:\/\/jensmeisner.net\/wp-content\/uploads\/2016\/11\/AfterOneDotSixOneEight_Exhibit_Ver2_129024_53888-1024x322.jpg 1024w, https:\/\/jensmeisner.net\/wp-content\/uploads\/2016\/11\/AfterOneDotSixOneEight_Exhibit_Ver2_129024_53888-300x94.jpg 300w, https:\/\/jensmeisner.net\/wp-content\/uploads\/2016\/11\/AfterOneDotSixOneEight_Exhibit_Ver2_129024_53888-768x241.jpg 768w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/p>\n<p><strong>SOURCE CODE:<\/strong><\/p>\n<p><a href=\"https:\/\/gitlab.com\/DigitalStages\/afteronedotsixoneeight\">https:\/\/gitlab.com\/DigitalStages\/afteronedotsixoneeight<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Diese Visualisierungssoftware berechnet eine Stelle der Fibonacci-Folge und ihre benachbarten Stellen. Die Division zweier benachbarter Stellen ergibt eine Zahl, auch Goldener Schnitt genannt. Die y-Achse stellt die berechneten Zahlen des Goldenen Schnitts gem\u00e4\u00df der Fibonacci-Folge dar, w\u00e4hrend die Dezimalstellen hinter dem Komma auf der x-Achse dargestellt sind. HINTERGRUND...<\/p>","protected":false},"author":1,"featured_media":136,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[49],"tags":[],"class_list":["post-132","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-code"],"rttpg_featured_image_url":{"full":["https:\/\/jensmeisner.net\/wp-content\/uploads\/2016\/11\/AfterOneDotSixOneEight_th.png",400,225,false],"landscape":["https:\/\/jensmeisner.net\/wp-content\/uploads\/2016\/11\/AfterOneDotSixOneEight_th.png",400,225,false],"portraits":["https:\/\/jensmeisner.net\/wp-content\/uploads\/2016\/11\/AfterOneDotSixOneEight_th.png",400,225,false],"thumbnail":["https:\/\/jensmeisner.net\/wp-content\/uploads\/2016\/11\/AfterOneDotSixOneEight_th-150x150.png",150,150,true],"medium":["https:\/\/jensmeisner.net\/wp-content\/uploads\/2016\/11\/AfterOneDotSixOneEight_th-300x169.png",300,169,true],"large":["https:\/\/jensmeisner.net\/wp-content\/uploads\/2016\/11\/AfterOneDotSixOneEight_th.png",400,225,false],"1536x1536":["https:\/\/jensmeisner.net\/wp-content\/uploads\/2016\/11\/AfterOneDotSixOneEight_th.png",400,225,false],"2048x2048":["https:\/\/jensmeisner.net\/wp-content\/uploads\/2016\/11\/AfterOneDotSixOneEight_th.png",400,225,false],"trp-custom-language-flag":["https:\/\/jensmeisner.net\/wp-content\/uploads\/2016\/11\/AfterOneDotSixOneEight_th.png",18,10,false],"post-thumbnail":["https:\/\/jensmeisner.net\/wp-content\/uploads\/2016\/11\/AfterOneDotSixOneEight_th-280x196.png",280,196,true],"cd-small":["https:\/\/jensmeisner.net\/wp-content\/uploads\/2016\/11\/AfterOneDotSixOneEight_th.png",150,84,false],"cd-medium":["https:\/\/jensmeisner.net\/wp-content\/uploads\/2016\/11\/AfterOneDotSixOneEight_th.png",400,225,false],"cd-standard":["https:\/\/jensmeisner.net\/wp-content\/uploads\/2016\/11\/AfterOneDotSixOneEight_th.png",400,225,false]},"rttpg_author":{"display_name":"Jens Meisner","author_link":"https:\/\/jensmeisner.net\/de\/author\/admin_jens\/"},"rttpg_comment":1,"rttpg_category":"<a href=\"https:\/\/jensmeisner.net\/de\/category\/code\/\" rel=\"category tag\">CODE<\/a>","rttpg_excerpt":"This visualization software calculates one position of the Fibonacci sequence, and its surrounding neighbors. The division of two neighbors creates a number, also known as Golden Ratio. The y axis represents this calculated numbers of the Golden Ratio according to the Fibonacci sequence, while its decimals behind the comma are shown along the x-axis. BACKGROUND&#46;&#46;&#46;","_links":{"self":[{"href":"https:\/\/jensmeisner.net\/de\/wp-json\/wp\/v2\/posts\/132","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/jensmeisner.net\/de\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/jensmeisner.net\/de\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/jensmeisner.net\/de\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/jensmeisner.net\/de\/wp-json\/wp\/v2\/comments?post=132"}],"version-history":[{"count":41,"href":"https:\/\/jensmeisner.net\/de\/wp-json\/wp\/v2\/posts\/132\/revisions"}],"predecessor-version":[{"id":1264,"href":"https:\/\/jensmeisner.net\/de\/wp-json\/wp\/v2\/posts\/132\/revisions\/1264"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/jensmeisner.net\/de\/wp-json\/wp\/v2\/media\/136"}],"wp:attachment":[{"href":"https:\/\/jensmeisner.net\/de\/wp-json\/wp\/v2\/media?parent=132"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/jensmeisner.net\/de\/wp-json\/wp\/v2\/categories?post=132"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/jensmeisner.net\/de\/wp-json\/wp\/v2\/tags?post=132"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}