{"id":632,"date":"2017-09-03T22:27:10","date_gmt":"2017-09-04T02:27:10","guid":{"rendered":"https:\/\/geekhaus.com\/math103_fall2017\/?p=632"},"modified":"2017-10-11T11:27:11","modified_gmt":"2017-10-11T15:27:11","slug":"koch-snowflake-fractal","status":"publish","type":"post","link":"https:\/\/geekhaus.com\/math103_fall2017\/2017\/09\/03\/koch-snowflake-fractal\/","title":{"rendered":"Koch Snowflake"},"content":{"rendered":"

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According to Wikipedia, a fractal is a curve or geometric figure which has the same statistical character as the whole. \u00a0The definition goes further, calling on the snowflake as a primary example of what a fractal is, because similar patterns recur at progressively smaller scales. \u00a0Looking at chapter 1 of\u00a0Fractals: A Very Short Introduction<\/em> by Kenneth Falconer, the von Koch curve is one of the first fractals discussed. \u00a0It was first defined in 1904 by Helge von Koch. \u00a0The von Koch curve is how the snowflake design comes about.<\/p>\n

The pattern that this fractal follows, outlined in\u00a0Fractals<\/em> by Falconer, is created by starting with an equilateral triangle, removing the inner third of each side, creating another equilateral triangle at the place where the side was removed, and repeating these steps infinitely many times.<\/p>\n

The reason I chose the Koch snowflake (vase) as my fractal design was because it is created following a simple rule or pattern, and the 3D vase design is simple yet beautiful. \u00a0The images above show a digital as well as real life picture of the Koch snowflake vase, created by the thingiverse user amitnehra (link here<\/a>). \u00a0The featured image for this post shows the pattern of what the vase would look like if you were looking straight down at it. \u00a0Since the Koch snowflake is a fairly simple fractal pattern, I anticipate that the 3D print of this vase should come out smoothly.<\/p>\n

3D Printing Results<\/strong><\/h2>\n

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The original vase print I wanted to make was too complex, and took too long to make in class. \u00a0So, I found a more simple koch snowflake fractal made by pmoews<\/a>. \u00a0The snowflake I printed is a level three (I think) because there are three different sized shapes inside of the snowflake.<\/p>\n

The following video shows the idea that the koch snowflake’s perimeter is infinite, while the area is finite.<\/p>\n