Math Art
Jeener's Flower

Jeener's Flower

Jeener's Flower is a minimal surface, given by a parametrisation, immersed.

Open Jeener's Flower in the interactive viewer →

aperiodic def-parametric immersed implemented minimal tradition-classical

Formula

x(u, v)
u3⁢cos⁡(3⁢v)3−u5⁢cos⁡(5⁢v)5\frac{u^{3} \cos\left(3 v\right)}{3} - \frac{u^{5} \cos\left(5 v\right)}{5}
y(u, v)
−(u3⁢sin⁡(3⁢v)3+u5⁢sin⁡(5⁢v)5)-\left(\frac{u^{3} \sin\left(3 v\right)}{3} + \frac{u^{5} \sin\left(5 v\right)}{5}\right)
z(u, v)
u4⁢cos⁡(4⁢v)2\frac{u^{4} \cos\left(4 v\right)}{2}

Properties

Family
minimal
Given by
a parametrisation
Curvature
zero mean curvature
Periodicity
not periodic
Ends
0
Embedding
immersed
Fidelity
exact
Exactness
elementary

Sources

Weierstrass data reproduced numerically against the shipped implementation (math_art/minsurf/zoo.py, row JEENER) by sampling g and dh over rings in the complex plane at the row's default parameters: g: matches over 144 complex samples (worst 0); dh: matches over 144 complex samples (worst 0).