Denver City Wire

The second talk of the Lunch with Western Scholars series was presented by mathematician Robert Cohen, Ph.D.  His hour-long presentation was about the creation and exploration of fractals, or, according to Oxford Languages, “a curve or geometric figure, each part of which has the same statistical character as the whole.” Cohen started his talk by defining mathematics as, “the search for and study of patterns,” then discussed the creation of fractals using patterns and how he uses them in his teachings.

Discovering a Love for Fractals

Cohen discovered his love for fractals during his first sabbatical in 2014 when he was searching for a textbook for one of the classes he was teaching. One textbook gave him a “recipe” to put four mathematical transformations – reflection, rotation, dilation, and translation – in a “hat”, plot any point on a graph, pull a transformation out of the “hat” and use that transformation to plot a new point. The recipe said to repeat this process 10,000 times. Once finished, the transformed plots create a picture of a fern. The book said this would be the outcome every time no matter what the starting point was, what transformation was pulled, or what order the transformations were pulled in.

Falling Down a Rabbit Hole

“This was a very profound moment for me. After I followed this recipe, I needed to understand why this works. It completely derailed my sabbatical,” said Cohen. “I fell down this rabbit hole. I wanted to learn about how this fern was designed, how they knew this algorithm was going to work and if this random process was always going to develop the fern every time you ran it.”

Bringing it All to Western

After becoming an expert on the fern fractal and fractals in general, Cohen brought his knowledge to Western’s math students in a class all about fractals. While his talk barely scratches the surface, students in his fractal class learn the ins and outs of fractals and even how to create their own.

Western’s Lunch with the Scholars Series

Stay tuned for the next Lunch with Western Scholars talk. Limited seating provided – RSVP to ensure a spot.

Original source can be found here.