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Penrose Subdivision

Infinite 5-fold aperiodic Penrose tiling generated through recursive deflation of Robinson golden triangles using phi = (1+sqrt(5))/2.

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Live Parameters

Recursion Depth 4
Fractal deflation resolution
Rotation Drift 0.4
Aperiodic rotation speed
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Mathematical Formulation

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Analytical Equation
\phi = \frac{1+\sqrt{5}}{2}, \quad \mathbf{p}_{4} = \mathbf{p}_1 + \frac{\mathbf{p}_2 - \mathbf{p}_1}{\phi}
Compact Formula
p4 = p1 + (p2 - p1) / φ, subdivide(RobinsonTriangle(depth - 1))
Renderer Logic 
const p4x = x1 + (x2 - x1) / GOLDEN_RATIO;
const p4y = y1 + (y2 - y1) / GOLDEN_RATIO;
drawTriangle(ctx, x3, y3, p4x, p4y, x1, y1, depth - 1, 0, time);
drawTriangle(ctx, p4x, p4y, x3, y3, x2, y2, depth - 1, 1, time);
Open in Playground Zero Dependencies • Standalone

Mathematical Tags

#penrose #aperiodic #golden-ratio #fractal #tiling #geometry
Author: Math Art Core Target: 60 FPS

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