Math Visualization
Vectors, trigonometry, graphing, Fourier series, and fractals
Savitzky–Golay Smoothing
Noisy cosine vs SG(7,2) convolution — preserves peaks better than a wide boxcar.
Markov Chain (Weather)
Sun/Rain two-state chain: P matrix, stationary π, empirical vs theory.
Gradient Descent (2D)
Level sets of f(x,y) and path (x,y) ← (x,y) − η∇f; bowl or elliptic well.
Minkowski Diagram
Light cone and boosted axes in 1+1D; γ from v.
Twin Paradox
Out-and-back worldlines; proper time τ = T/γ vs Earth time T.
Monte Carlo π
Uniform samples in a square; 4·(in disk)/N estimates π.
Random Walk
1D or 2D steps; trail and running mean ⟨r²⟩ vs diffusion intuition.
Vector Addition
Place vectors and see the resultant with head-to-tail animation.
Trigonometry Circle
Unit circle with live sin, cos, tan values as you drag.
Function Grapher
Enter f(x) and see instant plots with zoom and pan.
Fourier Series
Build waveforms from sine waves. Add harmonics one by one.
Lissajous Curves
Beautiful patterns from two frequencies with adjustable ratio.
Harmonograph
Two damped harmonic sums in x and y: decaying rosette trace vs Lissajous loops.
Spirograph (Trochoids)
Hypo- or epitrochoid: fixed R, rolling r, pen d; hue trail and period hints.
Sandpile (SOC)
BTW abelian model: add grains, ≥4 topples to neighbors; critical avalanches.
Flow Field Particles
Synthetic v(x,y,t); advection with wrap; optional arrow grid.
Fractal Generator
Mandelbrot, Julia, Koch snowflake. Zoom infinitely.
a → v → x
Integrate acceleration to velocity and position; stacked time graphs.
Taylor Polynomial
sin, cos, or exp vs Taylor sum about center a up to order n.
Complex Phasor
exp(iωt) on the unit circle; Re, Im, and phase φ.
Least Squares Fit
Noisy linear data; fitted slope and intercept with residuals.
Convolution (pulses)
Two rectangular pulses; overlap length at τ = 0.
Euler vs RK4 (Pendulum)
Same nonlinear pendulum ODE and step h; Euler vs RK4 side by side.
Lotka–Volterra
N′ = αN−βNP, P′ = δNP−γP; phase plane RK4; equilibrium dot.
Logistic Growth
dN/dt = rN(1−N/K); exact S-curve vs carrying capacity K.
2×2 Matrix & Eigenvectors
Grid deformation under M; real λ eigen-direction arrows.