Orbitals

Generative fine-art homage to Dominikus Baur (@dominikus). A dense cluster of 3D-entangled beaded toroidal filaments coils around a hollow core, framed by high-contrast black and white slicing orbital tracks, floating eccentric satellite orbs, architectural ribbon wings with isoline cross-hatching, and an astrolabe dial on warm archival paper.

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60 FPS • Canvas 2D

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Full Executable Algorithm Code

23 lines 678 chars

// Orbitals (geometry)
ctx.fillStyle = 'rgba(6, 8, 12, 0.18)';
ctx.fillRect(0, 0, width, height);

const cx = width * 0.5;
const cy = height * 0.5;
const maxR = Math.min(width, height) * 0.38;
const t = time * 1.2;

ctx.beginPath();
const steps = 360;
for (let i = 0; i <= steps; i++) {
  const phi = (i / steps) * Math.PI * 2;
  const r = maxR * (0.6 + 0.3 * Math.sin(phi * 6 + t * 2) * Math.cos(phi * 4 - t));
  const px = cx + Math.cos(phi) * r;
  const py = cy + Math.sin(phi) * r;
  if (i === 0) ctx.moveTo(px, py);
  else ctx.lineTo(px, py);
}
ctx.closePath();
ctx.strokeStyle = 'hsla(' + ((time * 30 + 195) % 360) + ', 95%, 68%, 0.85)';
ctx.lineWidth = 2.2;
ctx.stroke();

Edit in Interactive Playground Zero Dependencies • Standalone Canvas 2D

Mathematical Formulation

high

Analytical Equation

\mathbf{r}(u,v) = \begin{pmatrix} (R + r\cos v)\cos u \\ (R + r\cos v)\sin u \\ r\sin v + \delta_z \end{pmatrix}, \quad \theta_k(t) = \omega_k t + \phi_k

Click to expand

Compact Formula

r(u,v) = ((R + r cos v)cos u, (R + r cos v)sin u, r sin v)

Mathematical Tags

#orbitals #astrolabe #dominikus #generative-art #torus-knot #monochrome #celestial #wireframe

Author: Dominikus Baur Tribute Target: 60 FPS

Orbitals

Full Executable Algorithm Code

Mathematical Formulation

Mathematical Tags

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