Quantum Mechanics
Atomic Orbital
When Desmos finally added 3-D graphing, I knew exactly what I wanted to build. For years I had only seen slices of orbitals—cross-sections and contour maps—but never the whole shape that surrounded the nucleus. The idea of watching those mathematical symmetries unfold in three dimensions was irresistible. I wanted to give the atom a form that could rotate, breathe, and change with its quantum numbers—the way I had always pictured it in my head.
Atomic Orbital Iterations
It began with confusion. In eighth grade, I saw a picture of atomic orbitals and couldn’t understand why atoms looked like that—why the shapes were so specific and symmetrical. When I watched Richard Behiel’s video on the hydrogen atom, the mystery deepened: every curve and node was the product of an equation. I wanted to rebuild those shapes from the ground up to see how math became matter. That curiosity launched my first true physics simulation.
Atomic Orbital 1
I wanted to see what really shapes an atom’s “probability cloud.” By visualizing the radial part of the Schrödinger equation, I showed how the wave function defines an electron’s distance from the nucleus. I built interactive sliders and graphs to connect math to intuition.
This graph taught me discipline and generality. Building reusable controls for every variable forced me to think like a designer, not just a student. It was my first large-scale physics project—made around ninth grade—and it showed me that abstraction becomes intuition only when you can teach it. The same design logic later shaped every project that followed.
Atomic Orbital 3
After building the separate radial and angular pieces, I wanted to see them interact. When the first combined probability plot appeared, it felt like the equations were painting the atom themselves. Using color and contours, I built a simulation that visualizes the full 3D probability density of an electron in hydrogen—proof that the math and the physics aligned.
This graph showed me how art and science can reflect each other. Each contour was a boundary of probability, and arranging them felt like composing with mathematics. It was also when I began thinking like an engineer—testing cases, logging errors, and validating results until the visualization held up. It taught me that persistence and structure are what turn curiosity into understanding.
Black Body Radiation
I wanted to understand why hotter objects emit bluer light and how that relationship could be shown in real, perceptual color. I built a graph that visualizes the full black-body spectrum for any temperature, with accurate intensity curves, visible-light wavelengths, and RGB mapping that follows the true Planckian locus.
This graph showed me that accessibility is part of accuracy. I first used it while teaching a short quantum mechanics unit, letting classmates explore how Planck’s equation predicts stellar colors. Their questions helped me refine labels, sliders, and color precision. I realized that the best simulations don’t just calculate—they invite curiosity and make complex ideas feel within reach.
Atomic Orbital 2
After finishing the radial wave function, I still didn’t understand why orbitals had distinct lobes and symmetries. Then I learned about spherical harmonics—angular patterns shaped by quantized momentum—and wanted to see them myself. I built a visualization to show how the quantum numbers l and m sculpt the electron cloud, aiming to balance accuracy with clarity and reveal symmetry in motion.
This graph taught me organization and persistence. As complexity grew, I had to carefully structure every file, formula, and notation. It also taught me humility—how even a tiny change in math could completely reshape the graph. It deepened my respect for the precision behind visualization and for how structure emerges from symmetry.
Atomic Orbital 4
This project brought everything together—the radial and angular components, the probability contours, and the layers of sliders and controls. Rendering it in 3-D meant turning mathematics into geometry. I wanted to see the real and imaginary parts separately, to understand not just where the electron might be but how its wave actually moves through space.
This graph showed me what mastery feels like. When the orbitals finally appeared—clean, balanced, and alive—I understood not just the hydrogen atom, but the process of understanding itself. True comprehension happens when intuition and algebra align. Using the graph later to teach my Honors Chemistry III class closed the loop between curiosity and communication.
Calabi Yau
After studying relativity and quantum mechanics, I wanted to go deeper into theories that try to unify them. String theory stood out for its elegance—and for the way it introduces extra dimensions. The Calabi–Yau manifold, the structure that allows those dimensions to fold in on themselves, felt like the perfect challenge: I wanted to make that geometry visible.
This graph showed me that even the most abstract physics can be explored through visualization. I learned that I don’t need to solve everything to understand it; sometimes intuition comes through shape and symmetry. In the future, I’d like to add iridescent coloring to reflect the way these manifolds are imagined in real string theory renderings.