Null Space Dynamics: Matrix Kernels & Superluminal Vacuum Fields
An investigation into the mathematics of matrix null spaces and their application to modeling electromagnetic vacuum field dynamics, metric warping, and Planck mass pair neutralization. Includes a live interactive 3D WebAssembly visualizer.
Hagen-Poiseuille Flow: Viscous Fluid Dynamics & Pipe Flow
An investigation into the physics of laminar viscous flow through rigid cylindrical pipes. We examine parabolic velocity profiles, the no-slip condition, temperature-dependent viscosity, and the clinical/industrial impact of the fourth-power law. Includes a live 2D/3D WASM visualizer.
Surface Integrals of Scalar Fields: Area Distortion & Numerical Integration
An investigation into the mathematics of integrating scalar functions over curved 2D manifolds embedded in 3D space. We analyze parametric mappings, local area scaling via the Jacobian determinant, and real-time numerical approximations. Includes a live 3D WASM visualizer.
Neural Byte: Evolutionary Agent Simulation in Rust
An analysis of Neural Byte, a high-performance 2D evolutionary simulation driven by feedforward neural networks and genetic selection algorithms. We examine the math behind sensory-based steering physics, Gaussian mutations, and metabolic dynamics. Includes a live WASM visualizer.
3D N-Body Systems: Octree Dynamics & Collision Detection
An investigation into modeling high-performance N-body systems in three dimensions. We analyze how Octree partitioning prunes gravitational interactions and accelerates elastic and merge collision checking. Includes a live 3D WASM visualizer.
Gabriel's Horn: Infinite Surface Area, Finite Volume
An analytical study of Gabriel's Horn (Torricelli's Trumpet). Explores the mathematical proofs of finite volume and infinite surface area, the resolution of the Painter's Paradox, and its educational relevance to calculus. Includes a live 3D WASM visualizer.
Visualizing Vector Fields: Topology, Calculus & Streamlines
An analytical exploration of 2D and 3D vector fields, focusing on streamlines, field topology, divergence, curl, and numerical integration schemes. Includes a live interactive streamline visualizer with real-time vector calculus HUD calculations.
Probability Calibration in Prediction Markets: Monte Carlo vs. ML
A comparative analysis of event probability calibration in prediction markets. Evaluates Monte Carlo simulations, artificial neural networks, and XGBoost tree ensembles, benchmarked on expected calibration error (ECE). Includes a live animated SDE simulator.
Denoising HFT Microstructure Noise: Causal Rolling Fourier Filters
An advanced mathematical signal engine and interactive visualization dashboard tailored for cleaning High-Frequency Trading (HFT) microstructure noise in real-time. Eliminates phase lag via mirrored Hann windowing.
Strange Attractors: Chaos & Geometry in Phase Space
A mathematical analysis and numerical simulation of 11 chaotic strange attractors. Covering the differential equations, fractal boundaries, RK4 numerical integration, and a real-time interactive phase-space simulator built in Rust.
Scaling Gravity: N-Body Simulation & Barnes-Hut
An exploration into building a high-performance N-body gravitational simulation in Rust. Utilizing QuadTree spatial partitioning to reduce complexity from O(n²) to O(n log n). Features a live WebAssembly sandbox.