{"id":2163,"date":"2017-11-13T22:52:47","date_gmt":"2017-11-14T03:52:47","guid":{"rendered":"https:\/\/geekhaus.com\/math103_fall2017\/?p=2163"},"modified":"2017-12-16T08:16:42","modified_gmt":"2017-12-16T13:16:42","slug":"film-fractal-carpet","status":"publish","type":"post","link":"https:\/\/geekhaus.com\/math103_fall2017\/2017\/11\/13\/film-fractal-carpet\/","title":{"rendered":"Film Fractal Carpet"},"content":{"rendered":"

The Film Fractal Carpet is made by removing four blocks, two opposing each other in pairs. The coordinates removed are (0,2), (0,3), (4,2), & (4,3). The sequence of \u00a0pictures shows the sequence from level 1-3.<\/p>\n

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Fractal Calculations<\/h3>\n

Before any calculations are done, look at this sample to know where some of the calculations come from.<\/p>\n

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Now you know know some of the math, here are the calculations of all three levels. Pictures are included for level 2 & 3.<\/p>\n

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Level 1: (1 x 4) = 4
\nLevel 2: (12 x 4) (1\/16) = 48 x 1\/16 = 3
\nLevel 3:\u00a0(144 x 4) (1\/16^2) = (576 x 1\/256) = 2.25<\/p>\n

The following photo shows the total combined surface area at level 3.<\/p>\n

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Calculating to Infinity<\/h3>\n

What would happen to infinity? Would there be a point where the fractal’s matter is too small to visually see? This picture will calculate the area if done at infinity. The strange part is the area is 0 because this fractal will constantly subtract matter until nothing remains.<\/p>\n

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The formula for calculation is A x [_1_]
\n[1-r]<\/p>\n

A = 4
\nR = (1\/2)(12)<\/p>\n

after simplifying the fraction portion of he formula, you end up with 4. Multiply that with A, which is also 4, to get 16. 16 is the initial area that a level 0 fractal carpet starts with, therefore, the area at infinity is 0.<\/p>\n

Fractal Dimension<\/h3>\n

This will sound strange, the fractal carpet is neither 1-dimensional nor 2-dimensional. So what is it then? The fractal lies in between, but first it must be calculated. Look at the photo below and explanation.<\/p>\n

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To start, you must know the numbers before the formula. The scale, the amount that each level divides by, is 1\/4th for each new level. The amount of copies is the amount of squares remaining from a new iteration, consult the first level to see this. Using the logarithm, log base 4 of 12, we get this long number.<\/p>\n

The dimension of this fractal is 1.79248125.<\/p>\n

Download Link<\/h3>\n

You can find the code from this Thingiverse link<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"

The Film Fractal Carpet is made by removing four blocks, two opposing each other in pairs. The coordinates removed are (0,2), (0,3), (4,2), & (4,3). The sequence of \u00a0pictures shows the sequence from level 1-3. Before any calculations are done, look at this sample to know where some […]<\/a><\/p>\n<\/div>","protected":false},"author":13,"featured_media":2164,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[44],"tags":[],"coauthors":[23],"_links":{"self":[{"href":"https:\/\/geekhaus.com\/math103_fall2017\/wp-json\/wp\/v2\/posts\/2163"}],"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\/13"}],"replies":[{"embeddable":true,"href":"https:\/\/geekhaus.com\/math103_fall2017\/wp-json\/wp\/v2\/comments?post=2163"}],"version-history":[{"count":19,"href":"https:\/\/geekhaus.com\/math103_fall2017\/wp-json\/wp\/v2\/posts\/2163\/revisions"}],"predecessor-version":[{"id":2914,"href":"https:\/\/geekhaus.com\/math103_fall2017\/wp-json\/wp\/v2\/posts\/2163\/revisions\/2914"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/geekhaus.com\/math103_fall2017\/wp-json\/wp\/v2\/media\/2164"}],"wp:attachment":[{"href":"https:\/\/geekhaus.com\/math103_fall2017\/wp-json\/wp\/v2\/media?parent=2163"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/geekhaus.com\/math103_fall2017\/wp-json\/wp\/v2\/categories?post=2163"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/geekhaus.com\/math103_fall2017\/wp-json\/wp\/v2\/tags?post=2163"},{"taxonomy":"author","embeddable":true,"href":"https:\/\/geekhaus.com\/math103_fall2017\/wp-json\/wp\/v2\/coauthors?post=2163"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}