Posts Tagged ‘ Just for Fun ’

Animate snowfall in SAS

December 14, 2016
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Out of the bosom of the Air,     Out of the cloud-folds of her garments shaken, Over the woodlands brown and bare,     Over the harvest-fields forsaken,         Silent, and soft, and slow         Descends the snow. "Snow-flakes" by Henry Wadsworth Longfellow Happy holidays to all my readers! In my last post I showed

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Create a Koch snowflake with SAS

December 10, 2016
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I have a fondness for fractals. In previous articles, I've used SAS to create some of my favorite fractals, including a fractal Christmas tree and the "devil's staircase" (Cantor ) function. Because winter is almost here, I think it is time to construct the Koch snowflake fractal in SAS. A

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Cantor sets, the devil’s staircase, and probability

July 5, 2016
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Last week I blogged about how to draw the Cantor function in SAS. The Cantor function is used in mathematics as a pathological example of a function that is constant almost everywhere yet somehow manages to "climb upwards," thus earning the nickname "the devil's staircase." The Cantor function has three

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Visualize the Cantor function in SAS

June 29, 2016
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I was a freshman in college the first time I saw the Cantor middle-thirds set and the related Cantor "Devil's staircase" function. (Shown at left.) These constructions expanded my mind and led me to study fractals, real analysis, topology, and other mathematical areas. The Cantor function and the Cantor middle-thirds

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Lo, how a polar rose e’er blooming

December 16, 2015
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Lo how a rose e'er blooming From tender stem hath sprung As I write this blog post, a radio station is playing Chrismas music. One of my favorite Christmas songs is the old German hymn that many of us know as "Lo, How a Rose E're Blooming." I was humming

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Mathematical art (part 2): Unweaving matrices

September 4, 2015
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In my previous blog post, I showed how you can use SAS to program a "weaving" algorithm that takes an image, cuts it into strips, and weaves the strips together to create mathematical art. I used matrices and heat maps for the computations and visualization. At the end of the

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Mathematical art: Weaving matrices

September 2, 2015
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An artist friend of mine recently created a beautiful abstract image and described the process on her blog. She says that "after painting my initial square, I cut it into strips and split them down the middle, then wove them together.... I had no idea when I started piecing these

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The distribution of Pythagorean triples by angle

April 15, 2015
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Last week I was chatting with some mathematicians and I mentioned the blog post that I wrote last year on the distribution of Pythagorean triples. In my previous article, I showed that there is an algorithm that uses matrix multiplication to generate every primitive Pythagorean triple by starting with the

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