Tag: Fractal

Rick Wicklin 4
Animate snowfall in SAS

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

Rick Wicklin 4
Create a Koch snowflake with SAS

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

Rick Wicklin 4
Visualize the Cantor function in SAS

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

Rick Wicklin 6
Pascal's triangle in SAS

Pascal's triangle is the name given to the triangular array of binomial coefficients. The nth row is the set of coefficients in the expansion of the binomial expression (1 + x)n. Complicated stuff, right? Well, yes and no. Pascal's triangle is known to many school children who have never heard of polynomials

Rick Wicklin 7
A fractal Christmas tree in SAS

In my previous post, I described how to implement an iterated function system (IFS) in the SAS/IML language to draw fractals. I used the famous Barnsley fern example to illustrate the technique. At the end of the article I issued a challenge: can you construct an IFS whose fractal attractor