*activate time machine*
Dear 11-year-old me,
You are an awkward, nerdy little thing. You and your giant glasses and brain full of math and crazy ideas which for some reason are not making you popular. You want to do mathematical things but you don’t really have any idea what that means or how to make it happen, so instead you’re watching M*A*S*H episodes after school and wishing that you could be like Hawkeye Pierce, who unlike you can somehow pull off being smart and different and contrary while still connecting with other people.
I am just writing to let you know that in thirty years you’ll be the Mathematician-in-Residence at the National Museum of Mathematics and you’ll get to go to a fancy Gala and meet Alan Alda in person to tell him about an analog inverse-iteration Juila set constructor that you helped to create.
However, you will have to wear a dress. Sorry about that part.
P.S. The Juila set corresponding to z^2-1 can be realized by taking any complex number z and adding 1, then taking the square root, over and over again. This is called the inverse-iteration method, and one of the coolest things about it is that it is self-correcting; wherever you start from, this process will lead you closer and closer to the Juila set – and if you make a mistake then further iterations of add-one-and-take-the-square-root will get you back on course. For a complex number, taking the square root involves halving an angle and taking the square root of a distance from the origin. Glen Whitney from MoMath had the genius idea of making a clock-like linkage that does exactly that, and Tim Nissen and Larry Diamond figured out how to make a giant interactive version of that linkage assembly. Guests at last night’s Chaos Ball put LED lights on a felt board behind this analog linkage to form the Juila set image shown above.
P.P.S. Also, sorry, you’re still awkward and nerdy 30 years later, and that doesn’t seem like it will change anytime soon.