{"id":2056,"date":"2017-11-14T09:29:49","date_gmt":"2017-11-14T14:29:49","guid":{"rendered":"https:\/\/geekhaus.com\/math103_fall2017\/?p=2056"},"modified":"2017-12-15T13:11:08","modified_gmt":"2017-12-15T18:11:08","slug":"four-corner-fractal","status":"publish","type":"post","link":"https:\/\/geekhaus.com\/math103_fall2017\/2017\/11\/14\/four-corner-fractal\/","title":{"rendered":"Four Corner Fractal Carpet"},"content":{"rendered":"

\"\"<\/p>\n

To make my fractal I removed the four corners of the blank carpet. I removed the coordinates [0,0], [3,0], [0,3], and [3,3]. With each iteration the\u00a0 four corners of each square get removed. I designed my fractal this way because I wanted something neat and orderly looking. I liked the cross shape of the first iteration so I went with it.<\/p>\n

 <\/p>\n

\"\"<\/p>\n

I also was able to create a level 4 of the Four Corner Fractal:<\/p>\n

\"\"<\/p>\n

level 1: (16-4)-(12×4)(1\/16)<\/p>\n

Infinite Geometric Series Calculations<\/h3>\n

The infinite calculation of the fractal carpet if calculated on and on would end up with 0 because as you remove more and more squares from the fractal, eventually you run out of fractal.<\/p>\n

Infinite series:\u00a016 \u2013 [(4×1)+(4×12)(1\/16)+(4)(12\/16^2)+(4)(12\/16^3)…\u221e]<\/p>\n

Dimension Calculation<\/h3>\n

To get the dimension of the fractal carpet each iteration is 1\/4 the size of the one that came before it. When doing the calculation once you get 12 you plug it into the logarithm log base A of B, which gets you log base 4 of twelve and then you get dimension.<\/p>\n

S^D=1\/the number of copies<\/p>\n

(1\/4)^D=1\/12<\/p>\n

1\/(4^D)=1\/12<\/p>\n

4^D=12<\/p>\n

log4(12)=D<\/p>\n

D=1.792<\/p>\n","protected":false},"excerpt":{"rendered":"

To make my fractal I removed the four corners of the blank carpet. I removed the coordinates [0,0], [3,0], [0,3], and [3,3]. With each iteration the\u00a0 four corners of each square get removed. I designed my fractal this way because I wanted something neat and […]<\/a><\/p>\n<\/div>","protected":false},"author":19,"featured_media":2903,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[44],"tags":[],"coauthors":[18],"_links":{"self":[{"href":"https:\/\/geekhaus.com\/math103_fall2017\/wp-json\/wp\/v2\/posts\/2056"}],"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\/19"}],"replies":[{"embeddable":true,"href":"https:\/\/geekhaus.com\/math103_fall2017\/wp-json\/wp\/v2\/comments?post=2056"}],"version-history":[{"count":9,"href":"https:\/\/geekhaus.com\/math103_fall2017\/wp-json\/wp\/v2\/posts\/2056\/revisions"}],"predecessor-version":[{"id":2864,"href":"https:\/\/geekhaus.com\/math103_fall2017\/wp-json\/wp\/v2\/posts\/2056\/revisions\/2864"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/geekhaus.com\/math103_fall2017\/wp-json\/wp\/v2\/media\/2903"}],"wp:attachment":[{"href":"https:\/\/geekhaus.com\/math103_fall2017\/wp-json\/wp\/v2\/media?parent=2056"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/geekhaus.com\/math103_fall2017\/wp-json\/wp\/v2\/categories?post=2056"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/geekhaus.com\/math103_fall2017\/wp-json\/wp\/v2\/tags?post=2056"},{"taxonomy":"author","embeddable":true,"href":"https:\/\/geekhaus.com\/math103_fall2017\/wp-json\/wp\/v2\/coauthors?post=2056"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}