Hyperbolic Poincaré

Non-Euclidean Poincaré disk projection exhibiting infinite geometric tessellations compressing gracefully toward the boundary circle.

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60 FPS • Canvas 2D

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Live Parameters

Tessellation Symmetry (p) 7

Hyperbolic polygonal order

Rotation Drift 0.4

Non-Euclidean drift speed

Mathematical Formulation

61 chars medium

Analytical Equation

ds^2 = 4 \frac{dx^2 + dy^2}{(1 - (x^2 + y^2))^2}, \quad d(z_1, z_2) = 2 \tanh^{-1} \left| \frac{z_1 - z_2}{1 - \bar{z}_1 z_2} \right|

Compact Formula

r_hyp = R * tanh(l * 0.25 + 0.1 sin(t)), θ = 2πi / p*l + t/l

Renderer Logic

const hypRadius = radius * Math.tanh((l * 0.25) + Math.sin(t) * 0.1);
const arcX = cx + Math.cos(angle) * hypRadius;
const arcY = cy + Math.sin(angle) * hypRadius;
const arcR = (radius - hypRadius) * 0.5;

Open in Playground Zero Dependencies • Standalone

Mathematical Tags

#poincare #hyperbolic #non-euclidean #geometry #tessellation #conformal

Author: Math Art Core Target: 60 FPS

Hyperbolic Poincaré

Live Parameters

Mathematical Formulation

Mathematical Tags

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