{"id":821,"date":"2017-09-04T23:18:34","date_gmt":"2017-09-05T03:18:34","guid":{"rendered":"https:\/\/geekhaus.com\/math103_fall2017\/?p=821"},"modified":"2017-10-11T11:18:10","modified_gmt":"2017-10-11T15:18:10","slug":"quaternion-julia","status":"publish","type":"post","link":"https:\/\/geekhaus.com\/math103_fall2017\/2017\/09\/04\/quaternion-julia\/","title":{"rendered":"Quaternion Julia"},"content":{"rendered":"

The first fractal I want to print is the\u00a0Quaternion Julia fractal. According to an website <\/a>written by Paul Bourke: “A quaternion has two more complex components and might be written as q = r + a i + b j + c k where r, a, b, and c are real numbers. There are slightly more complicated relationships between i, j, and kA quaternion has two more complex components and might be written as q = r + a i + b j + c k where r, a, b, and c are real numbers. There are slightly more complicated relationships between i, j, and k<\/p>\n

i2 = j2 = k2 = -1<\/p>\n

i j = k \u00a0 \u00a0 j k = i<\/p>\n

k i = j \u00a0 \u00a0 j i = -k<\/p>\n

k j = -i \u00a0 \u00a0 \u00a0i k = -j.<\/p>\n

To generate a quaternion fractal a function is iterated zn+1 = f(zn) and if it tends to infinity then it is outside the Julia set, if it is bounded then it is inside the set.” I personally think this is a bit complicated, as I have forgotten a lot about complex and imaginary numbers but the concept regarding how it interacts with limits still makes sense to me.<\/p>\n

\"\"\u00a0\"\"\"\"<\/p>\n

After watching a few videos and reading up on the calculus behind this complex, but beautiful, fractal I found this video that looped the different stages of a Quaternion Julia fractal.<\/p>\n

https:\/\/youtu.be\/VkmqT6MQoDE<\/p>\n

This model was created by theswope on Thingiverse<\/a> with a very vague description not disclosing how he made it. It doesnt say how big the model is but i believe it is small, as it is very polygonal and he has other older versions that are not as printer friendly he called “tests”.<\/p>\n

<\/p>\n

When I printed this fractal, I had to shrink it down a lot and I printed it on the Afinia which added a ton of supports. I want to try and scale it up and printing it on the Ultimaker eventually to get a more accurate print.\u00a0My hand is visible for reference. Here<\/a> is my make on Thingiverse.\"\"<\/p>\n","protected":false},"excerpt":{"rendered":"

The first fractal I want to print is the\u00a0Quaternion Julia fractal. According to an website written by Paul Bourke: “A quaternion has two more complex components and might be written as q = r + a i + b j + c k where r, […]<\/a><\/p>\n<\/div>","protected":false},"author":17,"featured_media":824,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[10],"tags":[],"coauthors":[28],"_links":{"self":[{"href":"https:\/\/geekhaus.com\/math103_fall2017\/wp-json\/wp\/v2\/posts\/821"}],"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\/17"}],"replies":[{"embeddable":true,"href":"https:\/\/geekhaus.com\/math103_fall2017\/wp-json\/wp\/v2\/comments?post=821"}],"version-history":[{"count":17,"href":"https:\/\/geekhaus.com\/math103_fall2017\/wp-json\/wp\/v2\/posts\/821\/revisions"}],"predecessor-version":[{"id":1592,"href":"https:\/\/geekhaus.com\/math103_fall2017\/wp-json\/wp\/v2\/posts\/821\/revisions\/1592"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/geekhaus.com\/math103_fall2017\/wp-json\/wp\/v2\/media\/824"}],"wp:attachment":[{"href":"https:\/\/geekhaus.com\/math103_fall2017\/wp-json\/wp\/v2\/media?parent=821"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/geekhaus.com\/math103_fall2017\/wp-json\/wp\/v2\/categories?post=821"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/geekhaus.com\/math103_fall2017\/wp-json\/wp\/v2\/tags?post=821"},{"taxonomy":"author","embeddable":true,"href":"https:\/\/geekhaus.com\/math103_fall2017\/wp-json\/wp\/v2\/coauthors?post=821"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}