Archive for October 18th, 2010

Remembering the Father of Fractals

by Katie Bowell, Curator of Cultural Interpretation

Last Thursday, October 14th, mathematician Benoit Mandelbrot died. Even if you’re not familiar with the name, I bet you’re familiar with images of his work; Mandelbrot was the father of fractal geometry.

 

Mandelbrot set

 

According to Mandelbrot, a fractal is

a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole

Before Mandelbrot defined the term “fractal,” the split-able geometric shapes had been noticed by other mathematicians. However, because the shapes defied the rules of Euclidean geometry that governed so much of the world of mathematics, the funny, repeating patterns were classified as oddities; strange “outcasts” of math with unnatural properties. Mandelbrot brought these shapes together and, in the words of a song by Johnathan Coulton about the mathematician, showed that “infinite complexity could be described by simple rules.”

Mandelbrot’s work with fractals and the complexity of roughness is now used to explain, explore, inform and predict patterns in an astonishing number of disciplines: everything from the stock market to vascular surgery.

You may have even looked at some fractals today – they’re found throughout the natural world. Seashells, snowflakes, lightening, ferns, blood vessels, pineapples, mountain ranges, galaxies, shorelines, stalactites, stalagmites and many more natural objects all exhibit the characteristic repeating pattern of fractals. My favorite? Romanesco broccoli.

 

Now THAT'S a fractal!

 

And fractals aren’t just found in nature. Computer analysis of Jackson Pollock’s paintings has found fractal patterns within what at first may just look like paint splatters and dribbles, and composers are using the theories behind fractals to create new mathematical musical compositions.

Here’s Mandelbrot’s TED Talk, “Fractals and the Art of Roughness.”

And here’s a beautiful visual journey through fractals

Mandelbrot Fractal Set Trip To e214 HD from teamfresh on Vimeo.

Want to learn more about fractals? The best place to start is Mandelbrot’s The Fractal Geometry of Nature.

From the Archives: Rosalie Kelly Remembers – Walden

by Pat Walker, Research Assistant, Local History Archives

The Fort Collins Local History Archive has a large collection of Oral Histories taken in the early 1970s. Rosalie Kelley Remembers is a series of excerpts taken from an interview with Rosalie Kelly, a descendant of North Park pioneer families the Pinkhams and Allards, May 22, 1975.

Now I’m trying to think about different things that were interesting in Walden when I first went there. Well, I remember my first day of school. And – oh, it was an adventure to us. Guy and I had always played by ourselves. We didn’t have other kids to play with. And here were all these kids, there was eight grades and the four grades of high school in one little building. But oh, that seemed enormous to me. Now there are four, five, six buildings on that campus. That’s a regular little campus. But then, this was one school house. And a little girl that I didn’t know then, but have know all my life and she’s a life-long friend, came up and put her hands in mine – took ahold of mine and she said, “You’re a new little girl here, Rosalie. If you come out at recess with me, back behind the school house, I’ll tell you where babies come from.” (laughter) That was my memory of my first day at school. I said, “Well, you really don’t need to bother, because my mother’s already told me.” (laughter)

Another thing we enjoyed, and just had a ball when we first got there, was, if Mamma wasn’t along and Guy and I went over – we only lived about a block from Main Street – we’d run up and down those board sidewalks, so you’d hear them clatter, you know, and clang, but if she was around, there was no running on the board sidewalks.

There’s a little soda fountain in Dr. Fisher’s Pharmacy and we could go in there and for a nickel we could get and ice cream soda.

And we’d lived always on a ranch, you know, so my, that was something to get that ice cream soda.”

Walden School Classroom

Walden, Colorado August 4, 1903

The Snyder House Hotel, Walden, Colorado about 1910


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