ẋ = σ(y - x) ẏ = x(ρ - z) - y ż = xy - βz

Lorenz Attractor

x = A·sin(a·t + δ) y = B·sin(b·t)

Lissajous Curves

x = (R+r)·cos(t) - r·cos((R+r)/r·t) y = (R+r)·sin(t) - r·sin((R+r)/r·t)

Epicycloid

r = e^cos(θ) - 2·cos(4θ) + sin⁵(θ/12)

Butterfly Curve

x = 16·sin³(t) y = 13·cos(t) - 5·cos(2t) - 2·cos(3t) - cos(4t)

Heart Curve

r = a·cos(k·θ) or r = a·sin(k·θ)

Rose Curves

r = a + b·θ x = r·cos(θ), y = r·sin(θ)

Archimedean Spiral

f(x) = Σ(aₙ·sin(nx) + bₙ·cos(nx))

Fourier Series