{"id":2328,"date":"2017-11-15T19:15:29","date_gmt":"2017-11-16T00:15:29","guid":{"rendered":"https:\/\/geekhaus.com\/math103_fall2017\/?p=2328"},"modified":"2017-12-16T12:10:29","modified_gmt":"2017-12-16T17:10:29","slug":"space-invader-carpet-fractal","status":"publish","type":"post","link":"https:\/\/geekhaus.com\/math103_fall2017\/2017\/11\/15\/space-invader-carpet-fractal\/","title":{"rendered":"Space Invader Carpet Fractal"},"content":{"rendered":"

\"\"<\/p>\n

I named my fractal the Space Invader because the white color and shape reminds me of the aliens from the classic arcade game Space Invaders. When designing this fractal carpet, I did not have any specific shape in mind, but I knew I wanted a symmetrical fractal to work with. After removing the squares from points (0,1), (3,1), (1,3), and (2,3) I found a shape I was ready to work with. Calculating the surface area of Level 1 was fairly easy, seeing that I only had to subtract 4 from the total of 16. After that, Level 2 was my next problem to tackle. Because the smaller squares have an area of 1, the subtracted part of those smaller squares would be equal to 1\/16. Multiplying 4, 12, and 1\/16 and subtracting it from the area of Level 1 gave me the area for Level 2, which is 9. Level 3 was simple after finding Level 2. I needed to again multiply by 12 because there were now 12 smaller whole squares I was using, and multiply again by 1\/16 due to the fact that these squares were getting smaller at a constant rate. Multiplying 4, 144, and 1\/256 and again subtracting from the previous level gave me the area of Level 3, which ended up being 6.75. The picture below shows my work. Also included below is a picture of my Level 3 with the gridlines of a fully intact Level 1.<\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

The most difficult part of my calculations was easily finding the sum of the geometric series.<\/p>\n

In order to do this I needed to use the formula\u00a0 \u00a0a(1\/1-r). In my case, a=4 (the number of squares I had originally removed), and r= 3\/4 (because, after removing 4 from 16, we are left with 12\/16 which simplifies to 3\/4).<\/p>\n

The work below illustrates my process:<\/p>\n

\"\"<\/p>\n","protected":false},"excerpt":{"rendered":"

I named my fractal the Space Invader because the white color and shape reminds me of the aliens from the classic arcade game Space Invaders. When designing this fractal carpet, I did not have any specific shape in mind, but I knew I wanted a symmetrical fractal […]<\/a><\/p>\n<\/div>","protected":false},"author":10,"featured_media":2329,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[44],"tags":[],"coauthors":[29],"_links":{"self":[{"href":"https:\/\/geekhaus.com\/math103_fall2017\/wp-json\/wp\/v2\/posts\/2328"}],"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\/10"}],"replies":[{"embeddable":true,"href":"https:\/\/geekhaus.com\/math103_fall2017\/wp-json\/wp\/v2\/comments?post=2328"}],"version-history":[{"count":4,"href":"https:\/\/geekhaus.com\/math103_fall2017\/wp-json\/wp\/v2\/posts\/2328\/revisions"}],"predecessor-version":[{"id":2897,"href":"https:\/\/geekhaus.com\/math103_fall2017\/wp-json\/wp\/v2\/posts\/2328\/revisions\/2897"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/geekhaus.com\/math103_fall2017\/wp-json\/wp\/v2\/media\/2329"}],"wp:attachment":[{"href":"https:\/\/geekhaus.com\/math103_fall2017\/wp-json\/wp\/v2\/media?parent=2328"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/geekhaus.com\/math103_fall2017\/wp-json\/wp\/v2\/categories?post=2328"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/geekhaus.com\/math103_fall2017\/wp-json\/wp\/v2\/tags?post=2328"},{"taxonomy":"author","embeddable":true,"href":"https:\/\/geekhaus.com\/math103_fall2017\/wp-json\/wp\/v2\/coauthors?post=2328"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}