Math Art
Enneper-ended k-noid

Enneper-ended k-noid

Enneper-ended k-noid is a minimal surface, given by a Weierstrass representation, immersed.

Open Enneper-ended k-noid in the interactive viewer →

aperiodic def-weierstrass immersed implemented minimal tradition-classical

Formula

Gauss map g
(−1+zn)z\frac{\left(-1 + z^{n}\right)}{z}
Height differential dh
z−1+n+t⁢z−1+2⁢n(−1+zn)3\frac{z^{-1 + n} + t z^{-1 + 2 n}}{\left(-1 + z^{n}\right)^{3}}

Properties

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

Definition

Extracted from the shipped row's source by AST (complete multi-line lambdas, phi triple (dh = phi3, g = phi3/(phi1 - i*phi2), a Weierstrass-representation identity)) 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 ENNK) by sampling g and dh over rings in the complex plane at the row's default parameters: g: matches over 144 complex samples (worst 1.42e-15); dh: matches over 144 complex samples (worst 3.58e-15).