Math
Mathematical visualizers and experiments for patterns, chaos, curves, and systems.
The Math category collects mathematical visualizers and experiments that make abstract systems tangible. Each tool turns equations into interactive geometry you can watch evolve, tune, and export. The tools are not calculators — they are visual explorations of how mathematical structures behave over time.
Fourier Series converts a user-drawn path into its discrete Fourier coefficients and re-renders it as a sum of rotating epicycles. Draw a shape with your mouse, then crank up the number of terms and watch the approximation converge. It is a hands-on way to feel what the Fourier transform actually does, with visible overshoot at sharp corners that diminishes as you add higher-frequency terms.
Lorenz Attractor integrates the three coupled Lorenz ODEs in real time and renders the iconic butterfly-wing trajectory as a fading 3D trail. The default parameters (sigma=10, rho=28, beta=8/3) produce the classic chaotic attractor. Small changes in any parameter produce wildly different trajectories within seconds — a direct, visible demonstration of sensitive dependence on initial conditions and the defining property of chaos.
Both tools in this category run on 2D canvas with adjustable parameters in the right sidebar. Export to PNG or JPG captures the current frame for use in coursework, presentations, or documentation.
