March 2016, after about a whole year living in Florida, Julia decided that she needed a break from studying for her PhD exam. She asked around the department and Matthew and another fearless young man joined her on her trip to Universal Studios, Orlando. After many rounds of high-speed roller coasters, they got to know each other. After this fun trip, Julia started to get invitations to the board game nights held by her colleagues, Matthew included.
January 2018, as Julia was signing herself up for the Tutoring Lab as part of her teaching requirement, Matthew saw Julia's name on the schedule, so he signed up to work during the same period. Since this was the last period before lunch, naturally Matthew asked Julia to lunch every week after tutoring. Their little lunch dates involved many poke bowls, beef gyros, and of course, great conversations.
May 2018, at the Gainesville Regional Airport, right before Julia flew to Europe to join her parents for an epic summer, Matthew asked her to be his girlfriend. Their relationship thus started out long-distance. Thanks to modern technology, they skyped every week. However, she could not stop talking about her wonderful trips to the Scandinavian, Central Europe, and South Europe. Matthew listened most of the time and patiently waited for her to come back.
January 2020, Matthew and Julia took another trip to Universal Studios, but before they could decide on which roller coaster to ride, Matthew got down on his knee and popped the question. He told Julia that he felt Universal was the right place to propose because that was when he started falling in love with her. As for Julia, she could never feel luckier to be able to share her life with this man and speak their common nerdy language together.
Our wedding logo is an example of a mathematical object called a Julia Set. A Julia Set is a special subset of the Cartesian plane. In order to understand what a Julia Set is, you first need to know about complex numbers.
A complex number is a number of the form \(1 + 3i\) where \(i = \sqrt{-1}\). Even though the number \(i\,\) might seem weird, you can do arithmetic with complex numbers using the ordinary rules of algebra. There are two components of a complex number \(x + iy\,\), a real component \(x\) and an imaginary component \(y\,\). These two components can be thought of as \((x,\, y)\) coordinates, so you can think of a complex number as point.
Now suppose that \(c\,\) is a complex number and consider the function \(f_c(z) = z^2 + c\). This is a function which takes a complex number and returns a complex number, it maps the plane to itself. Roughly, the Julia Set of the function \(f_c\,\) is the boundary of the set of points in the plane which go to infinity under repeated application of \(f_c\,\). So to visualize this set we can pick a point \(z_0\) in the plane, then we compute \(z_k = f_c(z_{k-1})\) for \(1 \leq k \leq N \). If a point gets too far away from the origin of the plane, we stop because this point is apparently diverging. If \(k\) is the number of iterations we've done when we stop, then the ratio \(k / N\) can be used as a measure of how divergent a point is. This ratio is used to color the visualization. Since the Julia Set is the boundary of the set of divergent points, it is actually the infinitesimally thin curve between the brighter parts of the image and the darker background.
You can play around with different values of \(c\) in the visualization below. You can pan by clicking and dragging and zoom in and out by using your mouse wheel.
We have our wedding registry on Amazon. You can access it here.