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Lorenz Attractor
Lissajous Curves
Epicycloid
Butterfly Curve
Heart Curve
Rose Curves
Archimedean Spiral
Fourier Series
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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