A few lesson plans exist for teaching visual arts and self-similarity (objects that have the same pattern) that could be used after showing this lesson. Shodor has some free lesson plans for students in grades 4 through 8. High school students can learn recursion algorithms to create the Koch curve using Scratch for free. Educational technologist Dylan Ryder has also written about creating fractals. A beautiful app worth checking out is Starry Night Interactive App by media artist Petros Vrellis. Download it to your tablet and create your own version of Starry Night. Finally, don’t forget to check out TED-Ed’s original The Case of the Missing Fractals. Can you solve the case?

Really interested in mathematics? If you live in the New York-area, visit the Museum of Modern Math for more on math and visual arts.

Turbulence, unlike painting, is mostly a time-dependent phenomenon, and after some time, breaks statistical self-similarity that Kolmogorov predicted in the 1960s. To learn more about Kolmogorov’s predictions, Terry Tao provides a great overview of Kolmogorov’s power laws for turbulence.

In fluid mechanics, since we can't often solve the equation for flow patterns, we develop a system of scaling between the physical properties. This is called dimensional analysis. Want to find out more about the five-thirds law that the video references? Scroll through this website and learn

There are a few articles that outline patterns of turbulence in Van Gogh’s Starry Night. Flow by Philip Ball (p. 164-178) provides an excellent overview of the concept for a broad audience. Nature featured this article: Van Gogh painted perfect turbulence. Discover Magazine in 2006 featured another article on this topic called A Turbulent Mind. Learn how accurate Van Gogh’s turbulence was in his paintings. Finally, this article entitled: Troubled Mind and Perfect Turbulence, gives a great description of several of Van Gogh’s paintings. It also discusses how the impact of the painting on the viewer was measured using the concept of luminosity.

Acknowledgements
Natalya St. Clair would like to thank those who helped contribute their feedback to the script of this piece at Countryside School, Harvey Mudd College, Princeton, and University of Illinois in Urbana-Champaign, and, including Chris Antonsen, Arthur Benjamin, Andrew Bernoff, Wendy Cho, Likith Govindaiah, Jon Jacobsen, Carolyn Meldgin, Aaron Williams, and her students and colleagues.