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This series of images is of Caltrain and BART stations between Palo Alto and San Francisco. Each of them were technically challenging, but the fourth shot is particularly interesting as it was taken from the middle of the tracks. In initial experiments, I hung the camera from a roll of poster paper, wound into a cylinder and stuffed with shirts for structure, and dangled my makeshift boom arm over the tracks. Later, I switched to a tripod and was able to capture the fourth image. I'm proud of the composition and printing in each of these — particularly the first, third, and fourth.

This series comes from the second roll of film I ever shot, taken while hiking along the railroad in Henry Cowell Redwoods State Park with my friend Max. The unused tracks have been converted into a trail following the path of a river canyon. A couple miles down the trail, there is a path down the canyon to a series of pools, flanked by green moss and flecked stone and great redwoods above that. These pools are called the Garden of Eden. This series was my first, and the quality of printing reflects that. However, it is a initial project I am proud of.

This is the code for this website. It's quite simple, just a static site written in raw HTML, CSS, and JavaScript, but it has some neat aninations and tricks to avoid undesirable behavior. In particular, some modifications were necessary to ensure that the "slide" format of the home page wasn't messed up by the fact that mobile windows (particularly on Chrome) change size during scrolling (when the address bar disappears). You are welcome to use this code as a template with attribution.

rsltn (pronounced resolution) is a fast, beautiful, and functional development environment for writing math in Neovim. rsltn stands for Robin's System for LaTeX in Neovim, but the name also refers to the goal of the project, the resolution of the two main steps in the process of creating math: experimentation and exposition. Indeed, rsltn both improves the experience of quickly writing beautiful math with \(\LaTeX\) and provides tools for experimenting and computing in two interactive spaces (the Napkin and the Notebook) with seamless integration between them.

This animation was created using a grid of pixels in three colors: one representing rock, one representing paper, and one representing scissors. When pixels are mostly surrounded by pixels which “beat” them, they switch (so rock mostly surrounded by paper becomes paper, for example). The system evolves but never settles, as waves of rock, paper, and scissors cross the screen. The evolving seas and landmasses of each color form interesting semi-periodic patterns.

Chip-firing is a model in dynamical combinatorics in which chips are passed back and forth along the edges of a graph. By considering the set of possible configurations and their combinations, one can construct the ‘‘sandpile group’’ of a graph. The identities of these groups have a beautiful fractal-esque structure which can be visualized for certain types of graphs. In this project, I computed the identities of sandpile groups for grid graphs beyond the sizes calculated in the past (e.g. in Klivan's The Mathematics of Chip-firing), culminating in the \(2000 \times 2000\) grid graph.

This image depicts the Julia set (that is, the set of initial values which remain bounded under iteration) of the function \(c(x) = \frac{7x + 2 - (5x + 2)\cos(\pi x)}{4}\). This function is a holomorphic extension of the Collatz function, which is initially defined as \(\frac{n}{2}\) if \(n\) is even and \(3n + 1\) if \(n\) is odd. The Collatz function is most famous for its role in the Collatz conjecture, the frustratingly simple question of whether or not repeated iteration of the function will eventually reach 1 (visualized here as the horizontal black line at the center of the fractal).

exparrows is a simple \(\LaTeX\) package for inserting customizable arrows pointing to parts of your equations. Adapted from examples shared by Sibin Mohan on Twitter, exparrows can improve the readability of long equations by clarifying the role of each term in the equation.

This is the template that I have developed for creating a cirriculum vitae (CV) in \(\LaTeX\). This is a fork of Kumar Saurav’s resume template available here, simplified slightly and reorganized to fit the needs of an academic rather than industry CV.