Sacred Mandala

Multi-tiered rotational kaleidoscope mandalas built on concentric harmonic ellipses rotating with alternating angular frequencies.

Playground

60 FPS • Canvas 2D

Click + Drag to interact with field

Live Parameters

Rotational Symmetry (Folds) 12

Kaleidoscopic sector count

Spin Rate 0.5

Harmonic oscillation speed

Mathematical Formulation

76 chars low

Analytical Equation

\mathbf{R}(\theta_k) \mathbf{E}(a_r, b_r, \phi_r(t)), \quad \theta_k = \frac{2\pi k}{N}, \quad k \in \{0, \dots, N-1\}

Compact Formula

rotate(2πk / N), drawEllipse(0, r, w * (1 + 0.2 sin(2t + r)), h, rotOffset)

Renderer Logic

ctx.rotate((Math.PI * 2) / folds);
const petalW = ringRadius * 0.35 * (1 + 0.2 * Math.sin(t * 2 + r));
const petalH = (maxR / rings) * 1.4;
ctx.ellipse(0, ringRadius, petalW, petalH, ringOffset, 0, Math.PI * 2);

Open in Playground Zero Dependencies • Standalone

Mathematical Tags

#mandala #kaleidoscope #symmetry #sacred-geometry #polar #geometry

Author: Math Art Core Target: 60 FPS

Sacred Mandala

Live Parameters

Mathematical Formulation

Mathematical Tags

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