{"id":169,"date":"2025-08-04T15:21:31","date_gmt":"2025-08-04T15:21:31","guid":{"rendered":"https:\/\/fourthfoundation.org\/wp\/?p=169"},"modified":"2025-08-04T15:21:31","modified_gmt":"2025-08-04T15:21:31","slug":"frank-lloyd-wrights-use-of-apollonian-nets","status":"publish","type":"post","link":"https:\/\/workshophiraku.com\/?p=169","title":{"rendered":"Frank Lloyd Wright&#8217;s Use of Apollonian Nets"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">Once again,&nbsp;Paul Laseau and James Tice, authors of \u201cFrank Lloyd Wright, Between Principle and Form\u201d reveal an&nbsp;element of Frank Lloyd Wright&#8217;s fractal intuition. A fractal pattern called an &#8220;Apollonian Net&#8221; or &#8220;Apollonian Gasket&#8221; is composed of a triplet of circles, each of which is tangent to the others. A complete description can be found at <a href=\"http:\/\/mathworld.wolfram.com\/ApollonianGasket.html\" target=\"_blank\" rel=\"noopener\">Wolfram MathWorld<\/a>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">This is not as common as other fractals, but it still represents self-similarity of scale. The three circles do not necessarily have to be within another circle, as the MathWorld entry&nbsp;shows.<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter size-large wp-image-387\"><img decoding=\"async\" src=\"https:\/\/workshophiraku.com\/wp-content\/uploads\/2025\/08\/mandelbrot171-ticelaseau37-1024x483.jpg\" alt=\"\" class=\"wp-image-1487\"\/><figcaption class=\"wp-element-caption\">Apollonian Gasket or Apollonian Net, courtesy: Benoit Mandelbrot&#8217;s, &#8220;The Fractal Nature of Geometry,&#8221; p. 171<\/figcaption><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The image below is from Paul Laseau&#8217;s and James Tice&#8217;s book, p. 37. The left column shows a clear fractal pattern.<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter size-large wp-image-519\"><img decoding=\"async\" src=\"https:\/\/workshophiraku.com\/wp-content\/uploads\/2025\/08\/ticelaseau37-mandelbrot171-1024x801.jpg\" alt=\"\" class=\"wp-image-1488\"\/><figcaption class=\"wp-element-caption\">Frank Lloyd Wright&#8217;s Site Plans. Note the left column that resembles an Apollonian Net. Formed from triplets of circles, where each circle is tangent to the others.<\/figcaption><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Once again,&nbsp;Paul Laseau and James Tice, authors of \u201cFrank Lloyd Wright, Between Principle and Form\u201d reveal an&nbsp;element of Frank Lloyd Wright&#8217;s fractal intuition. A fractal pattern called an &#8220;Apollonian Net&#8221; or &#8220;Apollonian Gasket&#8221; is composed of a triplet of circles, each of which is tangent to the others. A complete description can be found at [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[4,5],"tags":[],"class_list":["post-169","post","type-post","status-publish","format-standard","hentry","category-fractals","category-frank-lloyd-wright"],"_links":{"self":[{"href":"https:\/\/workshophiraku.com\/index.php?rest_route=\/wp\/v2\/posts\/169","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/workshophiraku.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/workshophiraku.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/workshophiraku.com\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/workshophiraku.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=169"}],"version-history":[{"count":0,"href":"https:\/\/workshophiraku.com\/index.php?rest_route=\/wp\/v2\/posts\/169\/revisions"}],"wp:attachment":[{"href":"https:\/\/workshophiraku.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=169"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/workshophiraku.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=169"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/workshophiraku.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=169"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}