Superformula Bloom

Johan Gielis' 2D superformula generalization of the superellipse, producing complex biological flora geometries through harmonic powers.

Playground

60 FPS • Canvas 2D

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Live Parameters

Rotational Symmetry (m) 6

Number of morphological petals

Curvature Exponent (n1) 0.3

Overall boundary sharpness

Morph Speed 0.8

Rate of dimensional oscillation

Mathematical Formulation

51 chars medium

Analytical Equation

r(\phi) = \left( \left|\frac{\cos(m\phi/4)}{a}\right|^{n_2} + \left|\frac{\sin(m\phi/4)}{b}\right|^{n_3} \right)^{-\frac{1}{n_1}}

Compact Formula

r = (|cos(m*φ/4)/a|^n2 + |sin(m*φ/4)/b|^n3)^(-1/n1)

Renderer Logic

const part1 = Math.pow(Math.abs(Math.cos((m * phi) / 4) / a), n2);
const part2 = Math.pow(Math.abs(Math.sin((m * phi) / 4) / b), n3);
const r = Math.pow(part1 + part2, -1 / n1);
const px = cx + r * scale * Math.cos(phi + offset);
const py = cy + r * scale * Math.sin(phi + offset);

Open in Playground Zero Dependencies • Standalone

Mathematical Tags

#gielis #superformula #geometry #flower #polar #morphology

Author: Math Art Core Target: 60 FPS

Superformula Bloom

Live Parameters

Mathematical Formulation

Mathematical Tags

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