Dumbo Octopus Flight

Abyssal Grimpoteuthis octopus propulsion utilizing harmonic ear-like pectoral fin flapping kinematics and an undulating gelatinous cirrate umbrella skirt.

Playground

60 FPS • Canvas 2D

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Live Parameters

Ear Flap Rhythm 1.3

Pectoral fin flapping frequency

Pectoral Fin Wingspan 1.2

Ear-like fin extension scaling

Mathematical Formulation

112 chars medium

Analytical Equation

z_{\text{fin}}(u, t) = A_f \sin(\omega_f t) \cdot u + B_f \cos(\omega_f t) \cdot (1 - u^2), \quad \mathbf{p}_{\text{arm}}(k, t) = \mathbf{p}_0 + \begin{bmatrix} \sin\theta_k \cdot R_k \\ \cos\theta_k \cdot L_k + w_k(t) \end{bmatrix}

Compact Formula

ear_flap = bezierCurve(root, earCurl*15, earTip + earFlap*26), skirt = quadCurve(arm_prev, midPt - 10, arm_cur)

Renderer Logic

const earFlap = Math.sin(t * 3.2);
const tipY = rootY - 18 * earSpan * dumboScale + earFlap * (26 * dumboScale);
const armWave = Math.sin(t * 2.8 + a * 0.7) * 8 * dumboScale;
const armLen = (65 + (4 - Math.abs(a - 3.5)) * 8) * dumboScale;

Open in Playground Zero Dependencies • Standalone

Mathematical Tags

#dumbo-octopus #grimpoteuthis #deep-sea #abyss #creatures #fins #octopod

Author: Math Art Core Target: 60 FPS

Dumbo Octopus Flight

Live Parameters

Mathematical Formulation

Mathematical Tags

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