Math Art
Prismatic k-noid

Prismatic k-noid

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

Open Prismatic k-noid in the interactive viewer →

aperiodic def-weierstrass immersed implemented minimal tradition-classical

Formula

Gauss map g
z−1+n⁢(1−(z⁢a)n)an−zn\frac{z^{-1 + n} \left(1 - \left(z a\right)^{n}\right)}{a^{n} - z^{n}}
Height differential dh
z−1+n⁢(zn−an)⁢(zn−1an)(zn−bn)2⁢(zn−1bn)2\frac{z^{-1 + n} \left(z^{n} - a^{n}\right) \left(z^{n} - \frac{1}{a^{n}}\right)}{\left(z^{n} - b^{n}\right)^{2} \left(z^{n} - \frac{1}{b^{n}}\right)^{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_PRISM) by sampling g and dh over rings in the complex plane at the row's default parameters: g: matches over 144 complex samples (worst 3.97e-15); dh: matches over 144 complex samples (worst 3e-16).