Smoke Lattice Drift

Grid-based discretized fluid simulation capturing continuous harmonic injection, vortex dissipation, and buoyant plume dispersion.

Playground

60 FPS • Canvas 2D

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Live Parameters

Emission Speed 1

Turbulence oscillation rate

Mathematical Formulation

79 chars medium

Analytical Equation

\frac{\partial \rho}{\partial t} + \mathbf{u} \cdot \nabla \rho = \kappa \nabla^2 \rho + S(\mathbf{x}, t)

Compact Formula

ρ_{x,y}^{t+1} = ρ_{x,y}^t * 0.94 + sin(r*0.4 - 3t)*cos(4θ + 2t)*exp(-0.1r)*0.15

Renderer Logic

const injection = Math.sin(dist * 0.4 - t * 3) * Math.cos(Math.atan2(dy, dx) * 4 + t * 2) * Math.exp(-dist * 0.1);
density[idx] = Math.max(0, Math.min(1, density[idx] * 0.94 + injection * 0.15));

Open in Playground Zero Dependencies • Standalone

Mathematical Tags

#smoke #lattice #eulerian #fluid #diffusion #advection

Author: Math Art Core Target: 60 FPS

Smoke Lattice Drift

Live Parameters

Mathematical Formulation

Mathematical Tags

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