Coral Polyp Growth

Anthozoan coral colony morphology simulated through differential boundary growth equations and undulating feather tentacle radial symmetry.

Playground

60 FPS • Canvas 2D

Click + Drag to interact with field

Live Parameters

Tidal Wave Flow 0.8

Tentacle wave oscillation rate

Colony Expansion 1.1

Radial polyp size multiplier

Mathematical Formulation

94 chars medium

Analytical Equation

\mathbf{p}(\theta, t) = \left[ R_0 + \sum_{m=1}^{K} A_m \sin(m \theta + \omega_m t) \right] \begin{bmatrix} \cos\theta \\ \sin\theta \end{bmatrix}

Compact Formula

r_ridge = R0 + 12 sin(6θ + 0.5t) + 6 cos(12θ - t), tentacle = quadCurve(mouth, ctrlWave, tip)

Renderer Logic

const bump = Math.sin(phi * 6 + t * 0.5) * 12 + Math.cos(phi * 12 - t) * 6;
const r = (baseR * 0.6 + bump) * bloomScale;
const ctrlX = px + Math.cos(tentAngle) * (tentLen * 0.5) + Math.sin(wavePhase) * 6;

Open in Playground Zero Dependencies • Standalone

Mathematical Tags

#coral #polyps #differential-growth #botany #marine #nature

Author: Math Art Core Target: 60 FPS

Coral Polyp Growth

Live Parameters

Mathematical Formulation

Mathematical Tags

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