{"id":2722,"date":"2017-12-14T23:04:47","date_gmt":"2017-12-15T04:04:47","guid":{"rendered":"https:\/\/geekhaus.com\/math103_fall2017\/?p=2722"},"modified":"2017-12-16T16:55:10","modified_gmt":"2017-12-16T21:55:10","slug":"fractal-menagerie","status":"publish","type":"post","link":"https:\/\/geekhaus.com\/math103_fall2017\/2017\/12\/14\/fractal-menagerie\/","title":{"rendered":"Fractal Menagerie"},"content":{"rendered":"

\"\"<\/h3>\n

Group Members<\/h2>\n

Maddy Biggins<\/p>\n

Cat Falvey<\/p>\n

Yang Zhou<\/p>\n

Fractals<\/h2>\n

A fractal is a curve or geometric figure which parts’ have the same statistical characteristics as the whole.\u00a0 Fractals follow patterns or rules that recur at progressively larger or smaller scales.\u00a0 An iteration is one repetition of this rule, and fractals have many iterations or levels.\u00a0 As a part of this class we were first asked to research fractals, and find ones that we found interesting.\u00a0 We were then asked to come up with our own rule and create our own fractals.\u00a0 This menagerie contains many of the fractals that were found and created over the course of this class.\u00a0 As a part of these projects we made calculations and prints of our fractals.\u00a0 Some of the calculations we made were for perimeter, area, length, and dimension.\u00a0 With more complex objects these calculations were very difficult, but below we were able to illustrate more simple calculations that are easy to follow.<\/p>\n

Perimeter<\/h2>\n

\"\"<\/p>\n

The koch snowflake is one of the most famous and well documented fractals in mathematics.\u00a0 It is based off of the von koch curve.\u00a0 This fractal has an infinite perimeter.\u00a0 We got the 4\/5 value for calculations since each side of the triangle is being divided into thirds.<\/p>\n

Level 0<\/strong><\/p>\n

P=(4\/3)^0 x 3<\/p>\n

P=1(3)=3<\/p>\n

Level 1<\/strong><\/p>\n

P=(4\/3)^1 x 3<\/p>\n

P=(4\/3) x (3\/1) = 12\/3<\/p>\n

P=4<\/p>\n

Level 2<\/strong><\/p>\n

P=(4\/3)^2 x 3<\/p>\n

P=(16\/9) x (3\/1) = 48\/9<\/p>\n

P=16\/3<\/p>\n

Area<\/h2>\n

\"\"<\/p>\n

The area of this fractal is finite because its decimal value only goes up slightly every iteration, so it will continue to not exceed a bounded area.<\/p>\n

\"\"<\/p>\n

Showcase<\/h2>\n

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

A fractal is a curve or geometric figure which parts’ have the same statistical characteristics as the whole.\u00a0 Fractals follow patterns or rules that recur at progressively larger or smaller scales.\u00a0 An iteration is one repetition of this rule, and fractals have many iterations or levels […]<\/a><\/p>\n<\/div>","protected":false},"author":6,"featured_media":2724,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[45],"tags":[],"coauthors":[33],"_links":{"self":[{"href":"https:\/\/geekhaus.com\/math103_fall2017\/wp-json\/wp\/v2\/posts\/2722"}],"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\/6"}],"replies":[{"embeddable":true,"href":"https:\/\/geekhaus.com\/math103_fall2017\/wp-json\/wp\/v2\/comments?post=2722"}],"version-history":[{"count":6,"href":"https:\/\/geekhaus.com\/math103_fall2017\/wp-json\/wp\/v2\/posts\/2722\/revisions"}],"predecessor-version":[{"id":2941,"href":"https:\/\/geekhaus.com\/math103_fall2017\/wp-json\/wp\/v2\/posts\/2722\/revisions\/2941"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/geekhaus.com\/math103_fall2017\/wp-json\/wp\/v2\/media\/2724"}],"wp:attachment":[{"href":"https:\/\/geekhaus.com\/math103_fall2017\/wp-json\/wp\/v2\/media?parent=2722"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/geekhaus.com\/math103_fall2017\/wp-json\/wp\/v2\/categories?post=2722"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/geekhaus.com\/math103_fall2017\/wp-json\/wp\/v2\/tags?post=2722"},{"taxonomy":"author","embeddable":true,"href":"https:\/\/geekhaus.com\/math103_fall2017\/wp-json\/wp\/v2\/coauthors?post=2722"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}