Spiral Galaxy Density

Chia-Chiao Lin and Frank Shu's stellar density wave model explaining long-lived spiral arm patterns through quasi-stationary compression waves.

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60 FPS • Canvas 2D

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Live Parameters

Spiral Arm Count (m) 2

Number of density wave spiral arms

Arm Pitch Angle 0.22

Logarithmic winding tightness

Pattern Speed (Ωp) 0.6

Rigid wave pattern rotation

Mathematical Formulation

87 chars high

Analytical Equation

\Sigma(r, \theta, t) = \Sigma_0(r) + \Sigma_1(r) \cos\left[ m \left( \theta - \Omega_p t - f(r) \right) \right], \quad f(r) = \frac{\ln(r/r_0)}{\tan i}

Compact Formula

armPhase = (1/pitch) * ln(r/10) - 0.4t, r_eff = r * (1 - 0.12 * sin(m*(θ - armPhase)))

Renderer Logic

const armPhase = (1 / pitch) * Math.log(starR[i] / 10) - t * 0.4;
const distToArm = Math.sin(arms * (starTheta[i] - armPhase));
const effectiveR = starR[i] * (1 - 0.12 * distToArm);
const px = cx + Math.cos(starTheta[i]) * effectiveR * scale;
const py = cy + Math.sin(starTheta[i]) * effectiveR * scale;

Open in Playground Zero Dependencies • Standalone

Mathematical Tags

#galaxy #density-wave #astrophysics #spiral #space #stars

Author: Math Art Core Target: 60 FPS

Spiral Galaxy Density

Live Parameters

Mathematical Formulation

Mathematical Tags

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