{"id":646,"date":"2017-09-02T15:56:31","date_gmt":"2017-09-02T19:56:31","guid":{"rendered":"https:\/\/geekhaus.com\/math103_fall2017\/?p=646"},"modified":"2017-10-11T15:43:54","modified_gmt":"2017-10-11T19:43:54","slug":"honeycomb-hexagon","status":"publish","type":"post","link":"https:\/\/geekhaus.com\/math103_fall2017\/2017\/09\/02\/honeycomb-hexagon\/","title":{"rendered":"Honeycomb Hexagon"},"content":{"rendered":"<p>The very first fractal that I would like to print is called the Hexagonal fractal, and it is also known as the honeycomb fractal. There are actually different versions of the hexagonal fractal, however this particular one fascinates me the most because of its form and shape, resembling the honeycombs that bees make in nature. According to <a href=\"https:\/\/en.wikipedia.org\/wiki\/N-flake\">Wikipedia<\/a>, each Hexagonal fractal is formed by successive pieces of seven regular hexagons.\u00a0<sup id=\"cite_ref-4\" class=\"reference\"><\/sup>Each piece is also formed by placing a scaled hexagon in each corner and one in the center, the figure will be obtained because each iteration has 7 hexagons that are scaled by 1\/3. I&#8217;m still not quite sure what this means yet, but I&#8217;m hoping that I will learn more about it very soon.<\/p>\n<p>&nbsp;<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-647 size-full\" src=\"https:\/\/geekhaus.com\/math103_fall2017\/wp-content\/uploads\/2017\/09\/hexagonal-fractal_display_large_display_large.jpg\" alt=\"\" width=\"633\" height=\"536\" srcset=\"https:\/\/geekhaus.com\/math103_fall2017\/wp-content\/uploads\/2017\/09\/hexagonal-fractal_display_large_display_large.jpg 633w, https:\/\/geekhaus.com\/math103_fall2017\/wp-content\/uploads\/2017\/09\/hexagonal-fractal_display_large_display_large-300x254.jpg 300w\" sizes=\"(max-width: 633px) 100vw, 633px\" \/><\/p>\n<p>&nbsp;<\/p>\n<p>After looking at several pictures and information about the fractal, I realized how even though the whole thing looks very intricate, its parts have the same form and structure as the whole.\u00a0I think that it would be easy for me to set the dimension and size for this fractal since it is adjustable from the file in <a href=\"https:\/\/www.thingiverse.com\/thing:14023\">Thingiverse<\/a>. Hopefully I will get nice successful results once I start printing them, like the one shown in the picture below from <a href=\"https:\/\/www.thingiverse.com\/thing:14023\">Mechadense.\u00a0<\/a><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-648 size-full\" src=\"https:\/\/geekhaus.com\/math103_fall2017\/wp-content\/uploads\/2017\/09\/hexagon-fractal_display_large.jpg\" alt=\"\" width=\"800\" height=\"600\" srcset=\"https:\/\/geekhaus.com\/math103_fall2017\/wp-content\/uploads\/2017\/09\/hexagon-fractal_display_large.jpg 800w, https:\/\/geekhaus.com\/math103_fall2017\/wp-content\/uploads\/2017\/09\/hexagon-fractal_display_large-300x225.jpg 300w, https:\/\/geekhaus.com\/math103_fall2017\/wp-content\/uploads\/2017\/09\/hexagon-fractal_display_large-768x576.jpg 768w, https:\/\/geekhaus.com\/math103_fall2017\/wp-content\/uploads\/2017\/09\/hexagon-fractal_display_large-678x509.jpg 678w, https:\/\/geekhaus.com\/math103_fall2017\/wp-content\/uploads\/2017\/09\/hexagon-fractal_display_large-326x245.jpg 326w, https:\/\/geekhaus.com\/math103_fall2017\/wp-content\/uploads\/2017\/09\/hexagon-fractal_display_large-80x60.jpg 80w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<p>I also found a <a href=\"https:\/\/www.youtube.com\/watch?v=-abuxuhyoqY\">video<\/a> to help myself visualize my fractal, and it also shows how there are hexagonal patters that are always recurring:<\/p>\n<p><iframe loading=\"lazy\" title=\"Hexagon Fractal\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/-abuxuhyoqY?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>When I take a look at it the first time it was a little bit confusing because the video showed the patters quickly, but after a while I was able to put the video in slow motion and then I noticed how the fractal can be condensed into its previous shape and then if we want to expand it, then a copy of itself is made and this can go on an infinite number of times. I&#8217;m looking forward to try printing them, the only concern I have is that the structure might be a little bit fragile and some of the joints, but hopefully everything will turn out well.<\/p>\n<p><strong>3D Printing Results\u00a0<\/strong><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1695 size-full\" src=\"https:\/\/geekhaus.com\/math103_fall2017\/wp-content\/uploads\/2017\/09\/20171011_153702.jpg\" alt=\"\" width=\"4032\" height=\"3024\" srcset=\"https:\/\/geekhaus.com\/math103_fall2017\/wp-content\/uploads\/2017\/09\/20171011_153702.jpg 4032w, https:\/\/geekhaus.com\/math103_fall2017\/wp-content\/uploads\/2017\/09\/20171011_153702-300x225.jpg 300w, https:\/\/geekhaus.com\/math103_fall2017\/wp-content\/uploads\/2017\/09\/20171011_153702-768x576.jpg 768w, https:\/\/geekhaus.com\/math103_fall2017\/wp-content\/uploads\/2017\/09\/20171011_153702-1024x768.jpg 1024w, https:\/\/geekhaus.com\/math103_fall2017\/wp-content\/uploads\/2017\/09\/20171011_153702-678x509.jpg 678w, https:\/\/geekhaus.com\/math103_fall2017\/wp-content\/uploads\/2017\/09\/20171011_153702-326x245.jpg 326w, https:\/\/geekhaus.com\/math103_fall2017\/wp-content\/uploads\/2017\/09\/20171011_153702-80x60.jpg 80w\" sizes=\"(max-width: 4032px) 100vw, 4032px\" \/><\/p>\n<p>This image shows my final print design. I adjusted the size so that it would not print for a long period of time, in fact this print took me for only about forty five minutes. I wasn&#8217;t able to complete the whole printing process because there was a bit of a problem with the printer, however, even though the fractal wasn&#8217;t completely finished it still looks like the model that is shown on <a href=\"https:\/\/www.thingiverse.com\/thing:14023\">Thingiverse<\/a>. I posted a picture of my fractal on <a href=\"https:\/\/www.thingiverse.com\/make:379072\">Mechadense&#8217;s page<\/a>, which is the person who shared the fractal on Thingiverse. The honeycomb fractal is a bit more intricate than it looks, but I think that after doing my first attempt, I am more curious as to make a second attempt and hopefully this time it will come out perfectly.<\/p>\n","protected":false},"excerpt":{"rendered":"<div class=\"mh-excerpt\"><p>The very first fractal that I would like to print is called the Hexagonal fractal, and it is also known as the honeycomb fractal. There are actually different versions of the hexagonal fractal, however this particular one fascinates me the most because of its form <a class=\"mh-excerpt-more\" href=\"https:\/\/geekhaus.com\/math103_fall2017\/2017\/09\/02\/honeycomb-hexagon\/\" title=\"Honeycomb Hexagon\">[&#8230;]<\/a><\/p>\n<\/div>","protected":false},"author":26,"featured_media":647,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[10],"tags":[],"coauthors":[22],"_links":{"self":[{"href":"https:\/\/geekhaus.com\/math103_fall2017\/wp-json\/wp\/v2\/posts\/646"}],"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\/26"}],"replies":[{"embeddable":true,"href":"https:\/\/geekhaus.com\/math103_fall2017\/wp-json\/wp\/v2\/comments?post=646"}],"version-history":[{"count":8,"href":"https:\/\/geekhaus.com\/math103_fall2017\/wp-json\/wp\/v2\/posts\/646\/revisions"}],"predecessor-version":[{"id":1697,"href":"https:\/\/geekhaus.com\/math103_fall2017\/wp-json\/wp\/v2\/posts\/646\/revisions\/1697"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/geekhaus.com\/math103_fall2017\/wp-json\/wp\/v2\/media\/647"}],"wp:attachment":[{"href":"https:\/\/geekhaus.com\/math103_fall2017\/wp-json\/wp\/v2\/media?parent=646"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/geekhaus.com\/math103_fall2017\/wp-json\/wp\/v2\/categories?post=646"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/geekhaus.com\/math103_fall2017\/wp-json\/wp\/v2\/tags?post=646"},{"taxonomy":"author","embeddable":true,"href":"https:\/\/geekhaus.com\/math103_fall2017\/wp-json\/wp\/v2\/coauthors?post=646"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}