{"id":2363,"date":"2017-11-09T22:44:37","date_gmt":"2017-11-10T03:44:37","guid":{"rendered":"https:\/\/geekhaus.com\/math103_fall2017\/?p=2363"},"modified":"2017-12-15T12:21:41","modified_gmt":"2017-12-15T17:21:41","slug":"snowflake-carpet-fractal","status":"publish","type":"post","link":"https:\/\/geekhaus.com\/math103_fall2017\/2017\/11\/09\/snowflake-carpet-fractal\/","title":{"rendered":"Snowflake Carpet Fractal"},"content":{"rendered":"<h2>Project Idea<\/h2>\n<p>I am calling this the snowflake carpet fractal because the higher the levels go for this fractal, the more it looks like a snowflake.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-2379 size-full\" src=\"https:\/\/geekhaus.com\/math103_fall2017\/wp-content\/uploads\/2017\/11\/image1.jpeg\" alt=\"\" width=\"4032\" height=\"3024\" srcset=\"https:\/\/geekhaus.com\/math103_fall2017\/wp-content\/uploads\/2017\/11\/image1.jpeg 4032w, https:\/\/geekhaus.com\/math103_fall2017\/wp-content\/uploads\/2017\/11\/image1-300x225.jpeg 300w, https:\/\/geekhaus.com\/math103_fall2017\/wp-content\/uploads\/2017\/11\/image1-768x576.jpeg 768w, https:\/\/geekhaus.com\/math103_fall2017\/wp-content\/uploads\/2017\/11\/image1-1024x768.jpeg 1024w, https:\/\/geekhaus.com\/math103_fall2017\/wp-content\/uploads\/2017\/11\/image1-678x509.jpeg 678w, https:\/\/geekhaus.com\/math103_fall2017\/wp-content\/uploads\/2017\/11\/image1-326x245.jpeg 326w, https:\/\/geekhaus.com\/math103_fall2017\/wp-content\/uploads\/2017\/11\/image1-80x60.jpeg 80w\" sizes=\"(max-width: 4032px) 100vw, 4032px\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-2381 size-full\" src=\"https:\/\/geekhaus.com\/math103_fall2017\/wp-content\/uploads\/2017\/11\/image2.jpeg\" alt=\"\" width=\"4032\" height=\"3024\" srcset=\"https:\/\/geekhaus.com\/math103_fall2017\/wp-content\/uploads\/2017\/11\/image2.jpeg 4032w, https:\/\/geekhaus.com\/math103_fall2017\/wp-content\/uploads\/2017\/11\/image2-300x225.jpeg 300w, https:\/\/geekhaus.com\/math103_fall2017\/wp-content\/uploads\/2017\/11\/image2-768x576.jpeg 768w, https:\/\/geekhaus.com\/math103_fall2017\/wp-content\/uploads\/2017\/11\/image2-1024x768.jpeg 1024w, https:\/\/geekhaus.com\/math103_fall2017\/wp-content\/uploads\/2017\/11\/image2-678x509.jpeg 678w, https:\/\/geekhaus.com\/math103_fall2017\/wp-content\/uploads\/2017\/11\/image2-326x245.jpeg 326w, https:\/\/geekhaus.com\/math103_fall2017\/wp-content\/uploads\/2017\/11\/image2-80x60.jpeg 80w\" sizes=\"(max-width: 4032px) 100vw, 4032px\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-2382 size-full\" src=\"https:\/\/geekhaus.com\/math103_fall2017\/wp-content\/uploads\/2017\/11\/image3.jpeg\" alt=\"\" width=\"4032\" height=\"3024\" srcset=\"https:\/\/geekhaus.com\/math103_fall2017\/wp-content\/uploads\/2017\/11\/image3.jpeg 4032w, https:\/\/geekhaus.com\/math103_fall2017\/wp-content\/uploads\/2017\/11\/image3-300x225.jpeg 300w, https:\/\/geekhaus.com\/math103_fall2017\/wp-content\/uploads\/2017\/11\/image3-768x576.jpeg 768w, https:\/\/geekhaus.com\/math103_fall2017\/wp-content\/uploads\/2017\/11\/image3-1024x768.jpeg 1024w, https:\/\/geekhaus.com\/math103_fall2017\/wp-content\/uploads\/2017\/11\/image3-678x509.jpeg 678w, https:\/\/geekhaus.com\/math103_fall2017\/wp-content\/uploads\/2017\/11\/image3-326x245.jpeg 326w, https:\/\/geekhaus.com\/math103_fall2017\/wp-content\/uploads\/2017\/11\/image3-80x60.jpeg 80w\" sizes=\"(max-width: 4032px) 100vw, 4032px\" \/><\/p>\n<p>To make my carpet I took out (0,0) and (3,3).<\/p>\n<h2>Surface Area<\/h2>\n<p>Below is the equation I used to calculate the surface area of level 1, 2, and 3.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-2303\" src=\"https:\/\/geekhaus.com\/math103_fall2017\/wp-content\/uploads\/2017\/11\/formula3.jpg\" alt=\"\" width=\"218\" height=\"49\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-2302\" src=\"https:\/\/geekhaus.com\/math103_fall2017\/wp-content\/uploads\/2017\/11\/formula2.jpg\" alt=\"\" width=\"103\" height=\"67\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-2536 size-full\" src=\"https:\/\/geekhaus.com\/math103_fall2017\/wp-content\/uploads\/2017\/11\/image3-1-e1511808560372.jpeg\" alt=\"\" width=\"3024\" height=\"4032\" srcset=\"https:\/\/geekhaus.com\/math103_fall2017\/wp-content\/uploads\/2017\/11\/image3-1-e1511808560372.jpeg 3024w, https:\/\/geekhaus.com\/math103_fall2017\/wp-content\/uploads\/2017\/11\/image3-1-e1511808560372-225x300.jpeg 225w, https:\/\/geekhaus.com\/math103_fall2017\/wp-content\/uploads\/2017\/11\/image3-1-e1511808560372-768x1024.jpeg 768w\" sizes=\"(max-width: 3024px) 100vw, 3024px\" \/><\/p>\n<h2><\/h2>\n<h2>Dimension<\/h2>\n<p>This is the equation I used to solve for dimension.\u00a0 The scaling factor was 1\/4 and the number of copies was 14.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-2535 size-full\" src=\"https:\/\/geekhaus.com\/math103_fall2017\/wp-content\/uploads\/2017\/11\/image2-1.jpeg\" alt=\"\" width=\"2048\" height=\"1536\" srcset=\"https:\/\/geekhaus.com\/math103_fall2017\/wp-content\/uploads\/2017\/11\/image2-1.jpeg 2048w, https:\/\/geekhaus.com\/math103_fall2017\/wp-content\/uploads\/2017\/11\/image2-1-300x225.jpeg 300w, https:\/\/geekhaus.com\/math103_fall2017\/wp-content\/uploads\/2017\/11\/image2-1-768x576.jpeg 768w, https:\/\/geekhaus.com\/math103_fall2017\/wp-content\/uploads\/2017\/11\/image2-1-1024x768.jpeg 1024w, https:\/\/geekhaus.com\/math103_fall2017\/wp-content\/uploads\/2017\/11\/image2-1-678x509.jpeg 678w, https:\/\/geekhaus.com\/math103_fall2017\/wp-content\/uploads\/2017\/11\/image2-1-326x245.jpeg 326w, https:\/\/geekhaus.com\/math103_fall2017\/wp-content\/uploads\/2017\/11\/image2-1-80x60.jpeg 80w\" sizes=\"(max-width: 2048px) 100vw, 2048px\" \/><\/p>\n","protected":false},"excerpt":{"rendered":"<div class=\"mh-excerpt\"><p>I am calling this the snowflake carpet fractal because the higher the levels go for this fractal, the more it looks like a snowflake. To make my carpet I took out (0,0) and (3,3). Below is the equation I used to calculate the surface area of level 1, 2, and 3. <a class=\"mh-excerpt-more\" href=\"https:\/\/geekhaus.com\/math103_fall2017\/2017\/11\/09\/snowflake-carpet-fractal\/\" title=\"Snowflake Carpet Fractal\">[&#8230;]<\/a><\/p>\n<\/div>","protected":false},"author":6,"featured_media":2896,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[44],"tags":[],"coauthors":[33],"_links":{"self":[{"href":"https:\/\/geekhaus.com\/math103_fall2017\/wp-json\/wp\/v2\/posts\/2363"}],"collection":[{"href":"https:\/\/geekhaus.com\/math103_fall2017\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/geekhaus.com\/math103_fall2017\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/geekhaus.com\/math103_fall2017\/wp-json\/wp\/v2\/users\/6"}],"replies":[{"embeddable":true,"href":"https:\/\/geekhaus.com\/math103_fall2017\/wp-json\/wp\/v2\/comments?post=2363"}],"version-history":[{"count":7,"href":"https:\/\/geekhaus.com\/math103_fall2017\/wp-json\/wp\/v2\/posts\/2363\/revisions"}],"predecessor-version":[{"id":2895,"href":"https:\/\/geekhaus.com\/math103_fall2017\/wp-json\/wp\/v2\/posts\/2363\/revisions\/2895"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/geekhaus.com\/math103_fall2017\/wp-json\/wp\/v2\/media\/2896"}],"wp:attachment":[{"href":"https:\/\/geekhaus.com\/math103_fall2017\/wp-json\/wp\/v2\/media?parent=2363"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/geekhaus.com\/math103_fall2017\/wp-json\/wp\/v2\/categories?post=2363"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/geekhaus.com\/math103_fall2017\/wp-json\/wp\/v2\/tags?post=2363"},{"taxonomy":"author","embeddable":true,"href":"https:\/\/geekhaus.com\/math103_fall2017\/wp-json\/wp\/v2\/coauthors?post=2363"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}