Math Art
Double Enneper

Double Enneper

Double Enneper is a minimal surface, given by a Weierstrass representation, genus 0, 2 ends, immersed.

Open Double Enneper in the interactive viewer →

aperiodic def-weierstrass immersed implemented minimal tradition-classical

Formula

Gauss map g
z−1+n⁢(zn−ζn)−1+zn⁢ζn\frac{z^{-1 + n} \left(z^{n} - \zeta^{n}\right)}{-1 + z^{n} \zeta^{n}}
Height differential dh
−z−1−n⁢(−1+(z⁢ζ)n)⁢(zn−ζn)1+ζ2⁢n\frac{-z^{-1 - n} \left(-1 + \left(z \zeta\right)^{n}\right) \left(z^{n} - \zeta^{n}\right)}{1 + \zeta^{2 n}}

Properties

Family
minimal
Given by
a Weierstrass representation
Curvature
zero mean curvature
Periodicity
not periodic
Genus
0
Ends
2
Embedding
immersed
Fidelity
exact
Exactness
numerical-integral

Definition

Extracted from the shipped row's source by AST (complete multi-line lambdas, g/dh lambdas) and reproduced numerically against the shipped callables over the complex plane, exactly -- no scalar slack.

Sources

Weierstrass data reproduced numerically against the shipped implementation (math_art/minsurf/zoo.py, row DOUBLE_ENNEPER) by sampling g and dh over rings in the complex plane at the row's default parameters: g: matches over 144 complex samples (worst 9.49e-16); dh: matches over 144 complex samples (worst 1.34e-15).