This page contains several demonstrations of the math applets software library, which is used to make interactive mathematical visuals which embed directly into web or desktop environments. I see this as an enhancement to the traditional text-and-image-based nature of written mathematics. The software is very much a work-in-progress.
The software is heavily inspired by manim: in fact, several of the class names and abstractions come directly from manim. The most significant difference is that this library is designed for user-interactive web elements (hence written in Typescript), while manim is used for rendering videos. They are designed for different (but highly overlapping!) pedagogical purposes.
Wave equation: This page builds an intuition for the wave equation, and depicts some phenomena of the 2-dimensional wave equation, such as dipoles and interference patterns. I wrote this simulator to help me visualize the difference between the ray model and wave model of optics, and to visualize the reflective property of conic sections.
Random walks: A random walk on a lattice of dimension 1 or 2 will always return to its starting point. But a random walk on a lattice of dimension 3 or higher may never return. Why? This page is about visualizing and proving this theorem, and exploring its continuous analog (Brownian motion).
Sunrise equation: This page uses 3D geometry to visualize the calculation of sunrise and sunset times, among other things. I was inspired to write this page while thinking about how to calculate the energy absorbed by a solar panel over the course of a day.