Brownian Constellation

Continuous random walk nodes interconnected by proximity-based Euclidean distance thresholds, forming dynamic topological webs.

Playground

60 FPS • Canvas 2D

Click + Drag to interact with field

Live Parameters

Constellation Nodes 100

Total walking points

Connection Reach 80

Maximum proximity distance

Mathematical Formulation

67 chars medium

Analytical Equation

E = \{ (i, j) \mid \|\mathbf{p}_i - \mathbf{p}_j\| \le r_{\text{conn}} \}, \quad \alpha_{ij} = 1 - \frac{\|\mathbf{p}_i - \mathbf{p}_j\|^2}{r_{\text{conn}}^2}

Compact Formula

d = dist(p_i, p_j), if (d < R) drawLine(p_i, p_j, alpha = 1 - d/R)

Renderer Logic

const dx = px[j] - px[i];
const dy = py[j] - py[i];
const dSq = dx * dx + dy * dy;
if (dSq < maxDistSq) {
  const alpha = 1 - dSq / maxDistSq;
  ctx.strokeStyle = hsla(hue, 85, 60, alpha * 0.5);
}

Open in Playground Zero Dependencies • Standalone

Mathematical Tags

#graph #constellation #brownian #network #euclidean #particles

Author: Math Art Core Target: 60 FPS

Brownian Constellation

Live Parameters

Mathematical Formulation

Mathematical Tags

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