Boids Emergence

Complex self-organizing flocking dynamics emerging entirely from three simple local rules: alignment, cohesion, and separation.

Playground

60 FPS • Canvas 2D

Click + Drag to interact with field

Live Parameters

Boid Population 250

Total agent count

Mathematical Formulation

78 chars high

Analytical Equation

\mathbf{a}_i = w_a \mathbf{v}_{\text{align}} + w_c \mathbf{v}_{\text{cohere}} + w_s \mathbf{v}_{\text{separate}} + \mathbf{F}_{\text{center}}

Compact Formula

v += align * 0.05 + cohere * 0.005 + separate * 0.15, p += clamp(v, maxSpeed)

Renderer Logic

vx[i] += alignX * 0.05 + cohereX * 0.005 + separateX * 0.15;
vy[i] += alignY * 0.05 + cohereY * 0.005 + separateY * 0.15;
const speed = Math.sqrt(vx[i] * vx[i] + vy[i] * vy[i]);
if (speed > maxSpeed) {
  vx[i] = (vx[i] / speed) * maxSpeed;
  vy[i] = (vy[i] / speed) * maxSpeed;
}

Open in Playground Zero Dependencies • Standalone

Mathematical Tags

#boids #flocking #artificial-life #emergence #particles #vectors

Author: Math Art Core Target: 60 FPS

Boids Emergence

Live Parameters

Mathematical Formulation

Mathematical Tags

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