{"id":680,"date":"2017-09-03T13:17:43","date_gmt":"2017-09-03T17:17:43","guid":{"rendered":"https:\/\/geekhaus.com\/math103_fall2017\/?p=680"},"modified":"2017-10-11T11:35:21","modified_gmt":"2017-10-11T15:35:21","slug":"gosper-curve","status":"publish","type":"post","link":"https:\/\/geekhaus.com\/math103_fall2017\/2017\/09\/03\/gosper-curve\/","title":{"rendered":"Gosper Curve"},"content":{"rendered":"<p>My first fractal I want to print is the Gosper Curve. This is a space-filling fractal that is also known by the name &#8220;flowsnake&#8221; as a twist on the word snowflake. Similar to the dragon curve, the Gosper Curve is a fractal because it is constructed by repetition of a small basic shape. Below, you can see how the basic first step of the curve repeats to become the larger and more intricate Gosper Curve.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-683 aligncenter\" src=\"https:\/\/geekhaus.com\/math103_fall2017\/wp-content\/uploads\/2017\/09\/320px-Gosper_curve_1.svg_-300x300.png\" alt=\"\" width=\"197\" height=\"197\" srcset=\"https:\/\/geekhaus.com\/math103_fall2017\/wp-content\/uploads\/2017\/09\/320px-Gosper_curve_1.svg_-300x300.png 300w, https:\/\/geekhaus.com\/math103_fall2017\/wp-content\/uploads\/2017\/09\/320px-Gosper_curve_1.svg_-150x150.png 150w, https:\/\/geekhaus.com\/math103_fall2017\/wp-content\/uploads\/2017\/09\/320px-Gosper_curve_1.svg_.png 320w\" sizes=\"(max-width: 197px) 100vw, 197px\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-682 aligncenter\" src=\"https:\/\/geekhaus.com\/math103_fall2017\/wp-content\/uploads\/2017\/09\/gosper-curve-300x300.png\" alt=\"\" width=\"603\" height=\"603\" srcset=\"https:\/\/geekhaus.com\/math103_fall2017\/wp-content\/uploads\/2017\/09\/gosper-curve-300x300.png 300w, https:\/\/geekhaus.com\/math103_fall2017\/wp-content\/uploads\/2017\/09\/gosper-curve-150x150.png 150w, https:\/\/geekhaus.com\/math103_fall2017\/wp-content\/uploads\/2017\/09\/gosper-curve.png 320w\" sizes=\"(max-width: 603px) 100vw, 603px\" \/><\/p>\n<p>As I mentioned earlier, this is a space-filling curve and the space that is filled by the curve is called the Gosper island. Other than this, I was not able to understand many of the properties of this fractal.\u00a0I have found a simple YouTube video that demonstrates how the Gosper Curve grows:<\/p>\n<p><iframe loading=\"lazy\" title=\"Growing the Gosper Curve\" width=\"500\" height=\"375\" src=\"https:\/\/www.youtube.com\/embed\/UP4sVPCItak?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe><\/p>\n<p>I chose this fractal because it seemed like a relatively simple fractal to recreate. I also found some really cool designs of the Gosper Curve on Thingiverse, which you can check out <a href=\"https:\/\/www.thingiverse.com\/search?q=gosper+curve&amp;sa=&amp;dwh=1059ac37ddca97e\">here<\/a>. My favorite image that I found linked to the Gosper Curve is a puzzle that someone created by printing two variations of the curve and fitting them together. I believe that this fractal would successfully print because it is similar to the dragon curve, and it is a generally flat surface.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-688 size-full\" src=\"https:\/\/geekhaus.com\/math103_fall2017\/wp-content\/uploads\/2017\/09\/thingiverse-gosper-curve.jpg\" alt=\"\" width=\"628\" height=\"472\" srcset=\"https:\/\/geekhaus.com\/math103_fall2017\/wp-content\/uploads\/2017\/09\/thingiverse-gosper-curve.jpg 628w, https:\/\/geekhaus.com\/math103_fall2017\/wp-content\/uploads\/2017\/09\/thingiverse-gosper-curve-300x225.jpg 300w, https:\/\/geekhaus.com\/math103_fall2017\/wp-content\/uploads\/2017\/09\/thingiverse-gosper-curve-326x245.jpg 326w, https:\/\/geekhaus.com\/math103_fall2017\/wp-content\/uploads\/2017\/09\/thingiverse-gosper-curve-80x60.jpg 80w\" sizes=\"(max-width: 628px) 100vw, 628px\" \/><\/p>\n<h2><strong>3D Print Result<\/strong><\/h2>\n<p>The 3D print of my fractal was pretty successful. Once I broke off some of the strings (the little pieces in between the design) I was able to stretch the design out into a line because it is all one continuous piece. This print took around 50 minutes to make but I would love to see what a larger model would look like if time allowed. Sharing my completed print on <a href=\"https:\/\/www.thingiverse.com\/thing:2185763\">Thingiverse<\/a> with the creator was really cool, I hope they check out the version of their design I printed!<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-990 size-full\" src=\"https:\/\/geekhaus.com\/math103_fall2017\/wp-content\/uploads\/2017\/09\/first-fractal.png\" alt=\"\" width=\"796\" height=\"804\" srcset=\"https:\/\/geekhaus.com\/math103_fall2017\/wp-content\/uploads\/2017\/09\/first-fractal.png 796w, https:\/\/geekhaus.com\/math103_fall2017\/wp-content\/uploads\/2017\/09\/first-fractal-297x300.png 297w, https:\/\/geekhaus.com\/math103_fall2017\/wp-content\/uploads\/2017\/09\/first-fractal-768x776.png 768w\" sizes=\"(max-width: 796px) 100vw, 796px\" \/><\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<div class=\"mh-excerpt\"><p>My first fractal I want to print is the Gosper Curve. This is a space-filling fractal that is also known by the name &#8220;flowsnake&#8221; as a twist on the word snowflake. Similar to the dragon curve, the Gosper Curve is a fractal because it is <a class=\"mh-excerpt-more\" href=\"https:\/\/geekhaus.com\/math103_fall2017\/2017\/09\/03\/gosper-curve\/\" title=\"Gosper Curve\">[&#8230;]<\/a><\/p>\n<\/div>","protected":false},"author":18,"featured_media":682,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[10],"tags":[],"coauthors":[37],"_links":{"self":[{"href":"https:\/\/geekhaus.com\/math103_fall2017\/wp-json\/wp\/v2\/posts\/680"}],"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\/18"}],"replies":[{"embeddable":true,"href":"https:\/\/geekhaus.com\/math103_fall2017\/wp-json\/wp\/v2\/comments?post=680"}],"version-history":[{"count":12,"href":"https:\/\/geekhaus.com\/math103_fall2017\/wp-json\/wp\/v2\/posts\/680\/revisions"}],"predecessor-version":[{"id":1630,"href":"https:\/\/geekhaus.com\/math103_fall2017\/wp-json\/wp\/v2\/posts\/680\/revisions\/1630"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/geekhaus.com\/math103_fall2017\/wp-json\/wp\/v2\/media\/682"}],"wp:attachment":[{"href":"https:\/\/geekhaus.com\/math103_fall2017\/wp-json\/wp\/v2\/media?parent=680"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/geekhaus.com\/math103_fall2017\/wp-json\/wp\/v2\/categories?post=680"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/geekhaus.com\/math103_fall2017\/wp-json\/wp\/v2\/tags?post=680"},{"taxonomy":"author","embeddable":true,"href":"https:\/\/geekhaus.com\/math103_fall2017\/wp-json\/wp\/v2\/coauthors?post=680"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}