Math Visualization
Vectors, trigonometry, graphing, Fourier series, and fractals
STFT & Spectrogram
Slide a windowed FFT across the signal: chirps, two-tones, bursts. Tune window M, hop, type — see the time–frequency trade-off live.
Morlet Wavelet (CWT)
Continuous wavelet transform with the complex Morlet wavelet: scaleogram |W(s,t)|, log-frequency axis, cone of influence, adjustable ω₀ and scale range.
Butterworth / Chebyshev IIR
Design Butterworth, Chebyshev I/II LP/HP filters: |H(f)|, phase, impulse response, and z-plane pole–zero plot via bilinear transform.
Kalman Filter (1-D)
Recursive optimal estimation: noisy measurements, hidden truth, predict + update with Q and R; random-walk or constant-velocity model with ±2σ band and innovations.
Mandelbrot Deep Zoom
Drag/wheel deep zoom into the Mandelbrot set with smooth continuous coloring and named landmarks.
Julia Set Explorer
Pick c by clicking the embedded mini-Mandelbrot or animate c along a circle; Fatou dust vs connected sets.
Newton Fractal
Basins of attraction for Newton iteration on zⁿ−1 with adjustable relaxation ω.
Rössler Attractor
RK4 integration of ẋ=−y−z, ẏ=x+ay, ż=b+z(x−c); period-doubling cascade as c grows.
L-Systems (Turtle)
Lindenmayer string rewriting + turtle: Koch, Sierpinski, Hilbert, Heighway dragon, plant.
Bézier & de Casteljau
Drag control points; live recursive linear-interpolation scaffolding evaluates B(t).
Delaunay & Voronoi
Bowyer–Watson triangulation and dual Voronoi tessellation; click to add seeds, drag to move.
Physarum Slime (Agents)
~4500 agents follow a deposited chemoattractant: deposit + diffusion + decay + 3-sensor steering grow path networks.
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.
FFT Magnitude Spectrum
Paint or preset a 256-point signal; radix-2 FFT shows |X[k]| vs bin (DC to Nyquist).
2D Phase Portrait (ODE)
Direction field and click-to-trace trajectories for planar systems: harmonic, damped, saddle, nodes, foci, pendulum (RK4).
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.
SIR Epidemic Model
S + I + R = 1: βSI and γI; ℛ₀ ≈ β/γ, herd threshold 1 − 1/ℛ₀; RK4 time plot.
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.
Conway's Game of Life
B3/S23 on a torus: paint cells, run, step — glider, LWSS, Gosper gun, pulsar, and more.
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.
Chaos Game (Sierpiński)
Random vertex + midpoint walk; the attractor is the Sierpiński gasket — try RGB by vertex.
Lagrange vs Cubic Spline
Click knots: Lagrange polynomial vs natural cubic spline; Runge preset shows edge oscillations.
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.
Logistic Map Bifurcation
x_{n+1}=rx_n(1−x_n): scan r, plot attractors — period doubling to chaos (Feigenbaum cascade).
2×2 Matrix & Eigenvectors
Grid deformation under M; real λ eigen-direction arrows.
Lorenz Strange Attractor
σ, ρ, β ODEs; sensitive butterfly in (x,z) projection — RK4 trace.