{"id":5677,"date":"2016-08-15T11:29:28","date_gmt":"2016-08-15T15:29:28","guid":{"rendered":"http:\/\/orbittrap.ca\/?p=5677"},"modified":"2016-08-15T11:29:28","modified_gmt":"2016-08-15T15:29:28","slug":"fractals-are-the-mogao-caves-of-our-times","status":"publish","type":"post","link":"https:\/\/orbittrap.ca\/?p=5677","title":{"rendered":"Fractals are the Mogao Caves of our times"},"content":{"rendered":"<div id=\"attachment_5678\" style=\"width: 510px\" class=\"wp-caption aligncenter\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-5678\" class=\"size-full wp-image-5678\" src=\"https:\/\/i0.wp.com\/orbittrap.ca\/wp-content\/uploads\/2016\/08\/mogao01.jpg?resize=500%2C333\" alt=\"One of the many illustrated caves\" width=\"500\" height=\"333\" srcset=\"https:\/\/i0.wp.com\/orbittrap.ca\/wp-content\/uploads\/2016\/08\/mogao01.jpg?w=500&amp;ssl=1 500w, https:\/\/i0.wp.com\/orbittrap.ca\/wp-content\/uploads\/2016\/08\/mogao01.jpg?resize=150%2C100&amp;ssl=1 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><p id=\"caption-attachment-5678\" class=\"wp-caption-text\">One of the many illustrated Mogao Caves in northwestern China<\/p><\/div>\n<p>Alright, maybe it&#8217;s just me but the image above and just about everything else in the <a href=\"https:\/\/en.wikipedia.org\/wiki\/Mogao_Caves\">Mogao Caves<\/a> bears a strong visual resemblance to what I see in fractal programs.<\/p>\n<p><em>What I see in fractal programs:\u00a0 <\/em>That might be a new way of defining the term but I believe it&#8217;s the most relevant in the context of visual art. This is because fractal formulas when rendered exhibit a discernible style to them just like the work of a painter like Van Gogh or Gustav Klimt or an architect like Frank Lloyd Wright does.\u00a0 Think of all fractal images as the work of just one artist: would you not suspect he was possibly inspired by the type of artworks we see in the Mogao Caves?<\/p>\n<div id=\"attachment_5680\" style=\"width: 510px\" class=\"wp-caption aligncenter\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-5680\" class=\"wp-image-5680 size-full\" src=\"https:\/\/i0.wp.com\/orbittrap.ca\/wp-content\/uploads\/2016\/08\/mogao02.jpg?resize=500%2C375\" width=\"500\" height=\"375\" srcset=\"https:\/\/i0.wp.com\/orbittrap.ca\/wp-content\/uploads\/2016\/08\/mogao02.jpg?w=500&amp;ssl=1 500w, https:\/\/i0.wp.com\/orbittrap.ca\/wp-content\/uploads\/2016\/08\/mogao02.jpg?resize=150%2C113&amp;ssl=1 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><p id=\"caption-attachment-5680\" class=\"wp-caption-text\">Fractal made in Sterlingware 1.7<\/p><\/div>\n<p>So, what are the visual similarities?\u00a0 What&#8217;s the family resemblance between the Buddhist cave and the fractal image?<\/p>\n<p>Visual similarities<\/p>\n<ul>\n<li>Symmetry (left\/right mirror image)<\/li>\n<li>Hierarchical structure (the details support the &#8220;macro-tails&#8221;)<\/li>\n<li>Geometric (circles, squares, parabolas, shapes that are formulaic)<\/li>\n<li>Abstracted\/Symbolic (simplified and stylized but retaining a resemblance to real things, mainly natural: hills, sky, clouds, flowers,)<\/li>\n<\/ul>\n<p>It&#8217;s not just the visual style resemblance; illustrated caves seems to work like fractal programs too.<\/p>\n<p>Viewing environment similarities (caves and fractal programs, in general)<\/p>\n<ul>\n<li>Immersive (walk into a cave; zoom into a fractal)<\/li>\n<li>No frame (the whole image is uncontained and unconfined)<\/li>\n<li>Interactive (your head&#8217;s the frame; turn the head, change the composition; focus on a detail in a corner or the main structure in the center, or something you never noticed before)<\/li>\n<li>Variations on a theme (we see repeating shapes and structures; visual deja vu)<\/li>\n<li>No distractions (related to immersive; one can easily lose track of time, and space, in fractals because there is no real beginning or end; same for an illustrated cave)<\/li>\n<\/ul>\n<p>Notice the little, tiny buddha-circles on the side walls in the photo and the little red, dot-balls in the central area of the fractal, one the &#8220;walls&#8221; of the fractal?\u00a0 Obviously there&#8217;s no close fractal equivalent to the human form so all we can compare the statue of the Buddha in the center of the cave with is the prominent central shape that occurs very often in fractal images (especially in <a href=\"https:\/\/en.wikipedia.org\/wiki\/Sterling_(program)\">Sterling<\/a>).\u00a0 In this fractal it appears to be breaking out of a clearing in the clouds which frame it&#8217;s &#8220;head&#8221; like a garland of flowers or crown of brilliant clouds.<\/p>\n<div id=\"attachment_5681\" style=\"width: 510px\" class=\"wp-caption aligncenter\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-5681\" class=\"size-full wp-image-5681\" src=\"https:\/\/i0.wp.com\/orbittrap.ca\/wp-content\/uploads\/2016\/08\/mogao03.jpg?resize=500%2C349\" alt=\"Another of the Mogao Caves\" width=\"500\" height=\"349\" srcset=\"https:\/\/i0.wp.com\/orbittrap.ca\/wp-content\/uploads\/2016\/08\/mogao03.jpg?w=500&amp;ssl=1 500w, https:\/\/i0.wp.com\/orbittrap.ca\/wp-content\/uploads\/2016\/08\/mogao03.jpg?resize=150%2C105&amp;ssl=1 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><p id=\"caption-attachment-5681\" class=\"wp-caption-text\">Another of the Mogao Caves<\/p><\/div>\n<p>&nbsp;<\/p>\n<div id=\"attachment_5682\" style=\"width: 510px\" class=\"wp-caption aligncenter\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-5682\" class=\"size-full wp-image-5682\" src=\"https:\/\/i0.wp.com\/orbittrap.ca\/wp-content\/uploads\/2016\/08\/mogao4.jpg?resize=500%2C375\" alt=\"Another of the Sterlingware Caves\" width=\"500\" height=\"375\" srcset=\"https:\/\/i0.wp.com\/orbittrap.ca\/wp-content\/uploads\/2016\/08\/mogao4.jpg?w=500&amp;ssl=1 500w, https:\/\/i0.wp.com\/orbittrap.ca\/wp-content\/uploads\/2016\/08\/mogao4.jpg?resize=150%2C113&amp;ssl=1 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><p id=\"caption-attachment-5682\" class=\"wp-caption-text\">Another of the Sterling Caves<\/p><\/div>\n<p>The similarity comes from more than just the three niche elements; although you will notice that the fractal niches are all proportional and complimentary to each other like they are in the cave example.\u00a0 This is what I mean when I&#8217;ve said in previous postings that certain kinds of imagery are natural for fractal formulas to make.\u00a0 Symmetry, hierarchical order, and profuse detail and ornamentation come naturally to fractal images.\u00a0 The Buddhist art in the Mogao Caves (and elsewhere) exemplifies these same visual aspects for religious reasons to convey and express religious ideology.\u00a0 The are, in a sense, what I would call &#8220;Divine Diagrams&#8221; and it should come as no surprise to anyone familiar with fractals that fractal images often bear the same elements but, naturally, in a generic way.\u00a0 Fractal images could easily be used for symbolic purposes in a number of religious contexts.<\/p>\n<p>One interesting bit: notice in the fractal, below each of the niches, there are similar &#8220;stains&#8221; just as one sees below the niches in the cave photo.\u00a0 Perhaps it&#8217;s from burning candles or food offerings or some sort of weathering?\u00a0 In the fractal, of course, it&#8217;s just part of the formula rendering.<\/p>\n<p>A couple other similarities to point out:<\/p>\n<ul>\n<li>there is a vertical line structure\/feature extending up above the central niche in both the photo and the fractal<\/li>\n<li>all three niches have a framing element to them including a large, expanded framing element overtop of them in both images<\/li>\n<li>extending up from the two minor niches in the fractal are two obvious lines which meet a horizontal line just above them.\u00a0 This corresponds, to some extent, to the wall corners and the border of the edge of the ceiling in the cave image.\u00a0 It&#8217;s just a fluke that the fractal should look like it&#8217;s got walls and a ceiling but it&#8217;s expected that one should find such geometric elements in a fractal; in the cave they&#8217;re just ornamentation of the room&#8217;s structure which in this cave is square, rather than round.<\/li>\n<li>Notice what could pass as doorways on either side of the fractal on the edge of the image in line with the niches and real doorways in the photo.<\/li>\n<li>The geometrical, architectural element of the ledge in front of the cave&#8217;s niches is also found below the fractal&#8217;s niches.\u00a0 Again, geometric shapes occur naturally and frequently in fractals which cause them to easily support an architectural analogy because architecture is almost always geometrical.<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<div id=\"attachment_5683\" style=\"width: 510px\" class=\"wp-caption aligncenter\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-5683\" class=\"size-full wp-image-5683\" src=\"https:\/\/i0.wp.com\/orbittrap.ca\/wp-content\/uploads\/2016\/08\/mogao06.jpg?resize=500%2C360\" alt=\"Mogao Cave painting\" width=\"500\" height=\"360\" srcset=\"https:\/\/i0.wp.com\/orbittrap.ca\/wp-content\/uploads\/2016\/08\/mogao06.jpg?w=500&amp;ssl=1 500w, https:\/\/i0.wp.com\/orbittrap.ca\/wp-content\/uploads\/2016\/08\/mogao06.jpg?resize=150%2C108&amp;ssl=1 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><p id=\"caption-attachment-5683\" class=\"wp-caption-text\">Mogao Cave painting<\/p><\/div>\n<p>&nbsp;<\/p>\n<div id=\"attachment_5684\" style=\"width: 510px\" class=\"wp-caption aligncenter\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-5684\" class=\"size-full wp-image-5684\" src=\"https:\/\/i0.wp.com\/orbittrap.ca\/wp-content\/uploads\/2016\/08\/mogao05.jpg?resize=500%2C375\" alt=\"Fractal Cave painting\" width=\"500\" height=\"375\" srcset=\"https:\/\/i0.wp.com\/orbittrap.ca\/wp-content\/uploads\/2016\/08\/mogao05.jpg?w=500&amp;ssl=1 500w, https:\/\/i0.wp.com\/orbittrap.ca\/wp-content\/uploads\/2016\/08\/mogao05.jpg?resize=150%2C113&amp;ssl=1 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><p id=\"caption-attachment-5684\" class=\"wp-caption-text\">Fractal Cave painting<\/p><\/div>\n<p>&nbsp;<\/p>\n<div id=\"attachment_5685\" style=\"width: 385px\" class=\"wp-caption aligncenter\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-5685\" class=\"size-full wp-image-5685\" src=\"https:\/\/i0.wp.com\/orbittrap.ca\/wp-content\/uploads\/2016\/08\/image07.jpg?resize=375%2C500\" alt=\"Visvarupa Lokeshvara; not from the Mogao Caves but still Buddhist (or Hindu?)\" width=\"375\" height=\"500\" srcset=\"https:\/\/i0.wp.com\/orbittrap.ca\/wp-content\/uploads\/2016\/08\/image07.jpg?w=375&amp;ssl=1 375w, https:\/\/i0.wp.com\/orbittrap.ca\/wp-content\/uploads\/2016\/08\/image07.jpg?resize=113%2C150&amp;ssl=1 113w\" sizes=\"auto, (max-width: 375px) 100vw, 375px\" \/><p id=\"caption-attachment-5685\" class=\"wp-caption-text\">Visvarupa Lokeshvara; not from the Mogao Caves but still Buddhist or Hindu or both.<\/p><\/div>\n<p>Some of the same similarities occur here with respect to shapes, frames, borders, hierarchy; I think you get the idea now.\u00a0 I added the last one, a statue from somewhere, because it really emphasizes the design similarities between fractal imagery and these Buddhist paintings and statues.\u00a0 The last one looks so much like the fractal image that it&#8217;s hard to believe it came first.\u00a0 But this is my big point: the type of imagery that fractal programs produce has existed for centuries in the form of Buddhist religious imagery.\u00a0 And, if you&#8217;re familiar with religious art in general, many forms of religious art and symbolism have this fractal program resemblance .\u00a0 In fact, it has no particular correlation with any one religion, I just happened to notice it for the first time while browsing the Mogao Caves on the Wikipedia.<\/p>\n<p>I&#8217;m sure I&#8217;m not the first person to notice this fractal art \/ religious art connection.\u00a0 In my next post I expand the comparison of fractal imagery with the whole spectrum of religious art showing that the elements and style of religious art are in fact inherently fractal and therefore the sort of visual art that fractals produce easily, prolifically and to perfection.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Alright, maybe it&#8217;s just me but the image above and just about everything else in the Mogao Caves bears a strong visual resemblance to what I see in fractal programs. What I see in fractal programs:\u00a0 That might be a new way of defining the term but I believe it&#8217;s the most relevant in the &hellip; <a href=\"https:\/\/orbittrap.ca\/?p=5677\" class=\"more-link\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":5678,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[1],"tags":[],"class_list":["post-5677","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-uncategorized"],"jetpack_featured_media_url":"https:\/\/i0.wp.com\/orbittrap.ca\/wp-content\/uploads\/2016\/08\/mogao01.jpg?fit=500%2C333&ssl=1","jetpack-related-posts":[{"id":5672,"url":"https:\/\/orbittrap.ca\/?p=5672","url_meta":{"origin":5677,"position":0},"title":"Everything you need to know about Fractals and Art in one blog post","author":"Tim","date":"11 August, 2016","format":false,"excerpt":"Fractals are many things to many people but as an art form they're really very simple:\u00a0 Fractals are a visual medium. Do not be fooled by such simple language and such a simple statement,\u00a0 \"medium\" is the thin edge of the wedge that splits fractal art apart and reveals all\u2026","rel":"","context":"Similar post","block_context":{"text":"Similar post","link":""},"img":{"alt_text":"322px-Mandel_zoom_00_mandelbrot_set","src":"https:\/\/i0.wp.com\/orbittrap.ca\/wp-content\/uploads\/2016\/08\/322px-Mandel_zoom_00_mandelbrot_set.jpg?resize=350%2C200","width":350,"height":200},"classes":[]},{"id":5660,"url":"https:\/\/orbittrap.ca\/?p=5660","url_meta":{"origin":5677,"position":1},"title":"Galleries of the Gods","author":"Tim","date":"2 September, 2016","format":false,"excerpt":"As I said in my last post, there's something captivating about the Buddhist artworks in the Mogao caves in northwestern China and, strangely enough, I find it to be reminiscent of things I've seen in fractal programs.\u00a0 I've come up with a term for this electrifying visual genre: \"Divine Diagrams.\"\u00a0\u2026","rel":"","context":"Similar post","block_context":{"text":"Similar post","link":""},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/orbittrap.ca\/wp-content\/uploads\/2016\/08\/gallery01-e1472056403980.jpeg?fit=500%2C249&ssl=1&resize=350%2C200","width":350,"height":200},"classes":[]},{"id":365,"url":"https:\/\/orbittrap.ca\/?p=365","url_meta":{"origin":5677,"position":2},"title":"Sterling-Worlds &#8211; Interactive Fractal Art","author":"Tim","date":"18 February, 2009","format":false,"excerpt":"Climb the mountain, explore the caves, or check out the little islands off shore... Just load the parameter file (shellcity02.loo) into Sterling2 and this whole little world is yours.Fractals are a unique form of artistic imagery.\u00a0 They are more like sculptures and dioramas than the flat, static paintings they are\u2026","rel":"","context":"With 1 comment","block_context":{"text":"With 1 comment","link":"https:\/\/orbittrap.ca\/?p=365#comments"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":2130,"url":"https:\/\/orbittrap.ca\/?p=2130","url_meta":{"origin":5677,"position":3},"title":"UltraMeta: Snapshots from a fractal walkabout","author":"Tim","date":"18 December, 2010","format":false,"excerpt":"There's a lot of far-out stuff in Dan Wills' ultraMeta Picasa gallery. It's a reminder that fractal art can be just as much about exploring a fractal world as it is about that strange, fickle and formal thing called \"art.\"","rel":"","context":"With 4 comments","block_context":{"text":"With 4 comments","link":"https:\/\/orbittrap.ca\/?p=2130#comments"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/orbittrap.ca\/wp-content\/uploads\/2010\/12\/jovaNuliaTwo_dotdotdot_rev_went_catAttack_lerghe_siam_moonset_probe_pancake_openclose.jpg?fit=500%2C500&ssl=1&resize=350%2C200","width":350,"height":200},"classes":[]},{"id":362,"url":"https:\/\/orbittrap.ca\/?p=362","url_meta":{"origin":5677,"position":4},"title":"Fractal Woodburning","author":"Tim","date":"28 January, 2009","format":false,"excerpt":"I'm not making this up.\u00a0 I went surfing about to see what I could find in the fractal world and lo and behold at Flickr, a couple of pages into a search on the term \"fractal\", I saw wires, boards and strange, curly burn patterns.photo by AetherPhoto caption from Aether's\u2026","rel":"","context":"Similar post","block_context":{"text":"Similar post","link":""},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":5154,"url":"https:\/\/orbittrap.ca\/?p=5154","url_meta":{"origin":5677,"position":5},"title":"The Synthetic Aesthetic 2:  The Re-Introduction","author":"Tim","date":"29 August, 2013","format":false,"excerpt":"In the first part of this series, I introduced a few new ideas which have a central part to play in my concept of the Synthetic Aesthetic.\u00a0 I believe it might be of great benefit to pause and clarify those ideas before moving on to examples of actual artwork that\u2026","rel":"","context":"Similar post","block_context":{"text":"Similar post","link":""},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]}],"jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/orbittrap.ca\/index.php?rest_route=\/wp\/v2\/posts\/5677","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/orbittrap.ca\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/orbittrap.ca\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/orbittrap.ca\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/orbittrap.ca\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=5677"}],"version-history":[{"count":3,"href":"https:\/\/orbittrap.ca\/index.php?rest_route=\/wp\/v2\/posts\/5677\/revisions"}],"predecessor-version":[{"id":5688,"href":"https:\/\/orbittrap.ca\/index.php?rest_route=\/wp\/v2\/posts\/5677\/revisions\/5688"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/orbittrap.ca\/index.php?rest_route=\/wp\/v2\/media\/5678"}],"wp:attachment":[{"href":"https:\/\/orbittrap.ca\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=5677"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/orbittrap.ca\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=5677"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/orbittrap.ca\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=5677"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}