Mathematical Crab

Decapod crustacean mechanics featuring eight-legged inverse kinematic walking gaits, an elliptic carapace with marginal spines, and articulated pinching chelae.

Playground

60 FPS • Canvas 2D

Click + Drag to interact with field

Live Parameters

Gait Crawl Speed 1.4

Sideways walking cycle frequency

Claw Pinch Aperture 1

Chela finger opening amplitude

Mathematical Formulation

74 chars high

Analytical Equation

\mathbf{p}_{\text{knee}} = \mathbf{p}_{\text{coxa}} + \mathbf{R}(\theta_1) \mathbf{L}_1 + \mathbf{R}(\omega t + \phi_i) \mathbf{A}_{\text{lift}}

Compact Formula

knee = coxa + [cos(θ)*45 + reach, -20 + lift], pinch = 0.35 + 0.3*sin(3t)

Renderer Logic

const kneeLift = Math.sin(legPhase) * 14;
const kneeReach = Math.cos(legPhase) * 22;
const pinchAngle = (0.35 + 0.3 * Math.sin(t * 3 + side)) * clawPinch;

Open in Playground Zero Dependencies • Standalone

Mathematical Tags

#crab #crustacean #creatures #kinematics #gait #biomechanics

Author: Math Art Core Target: 60 FPS

Mathematical Crab

Live Parameters

Mathematical Formulation

Mathematical Tags

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