Bioluminescent Jellyfish

Marine cnidarian hydrostatic locomotion modeled via periodic radial bell contractions and multi-node sinusoidal wave propagation down trailing tentacles.

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60 FPS • Canvas 2D

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Live Parameters

Pulse Stroke Rate 1.2

Swimming bell contraction velocity

Tentacle Reach 160

Length of trailing cnidocyte tentacles

Bioluminescent Glow 1

Luciferin photonic emission level

Mathematical Formulation

74 chars high

Analytical Equation

R(\theta, t) = R_0 \left[ 1 + A \sin(\omega t) \cos(n \theta) \right], \quad y_{\text{tentacle}}(s, t) = s + A_t \sin(k s - \omega t)

Compact Formula

r_dome = R*(1 + 0.22*sin(3t)), y_tentacle = y0 + s + sin(3t - 6s + k)*18s

Renderer Logic

const marginFrill = 0.06 * Math.sin(phi * 12 + t * 4);
const px = cx + Math.cos(phi) * domeWidth * (1 + marginFrill);
const py = cy - Math.sin(phi) * domeHeight + marginFrill * 10;
const wave = Math.sin(t * 3 - normN * 6 + k * 0.5) * (18 * normN);

Open in Playground Zero Dependencies • Standalone

Mathematical Tags

#jellyfish #marine #creatures #bioluminescence #kinematics #waves

Author: Math Art Core Target: 60 FPS

Bioluminescent Jellyfish

Live Parameters

Mathematical Formulation

Mathematical Tags

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