Math Art
Lopez sphere (2 ends of index 2)

Lopez sphere (2 ends of index 2)

Lopez sphere (2 ends of index 2) is a minimal surface, given by a Weierstrass representation, immersed.

Open Lopez sphere (2 ends of index 2) in the interactive viewer →

aperiodic def-weierstrass immersed implemented minimal tradition-classical

Formula

Gauss map g
B⁢(1+z2+i⁢z⁢c)z\frac{B \left(1 + z^{2} + i z c\right)}{z}
Height differential dh
B⁢(i+i⁢z2−z⁢c)z2\frac{B \left(i + i z^{2} - z c\right)}{z^{2}}

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, 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 M3_LOPEZ) by sampling g and dh over rings in the complex plane at the row's default parameters: g: matches over 144 complex samples (worst 4.97e-16); dh: matches over 144 complex samples (worst 9.93e-16).