Bjorling: Logarithmic Spiral
Bjorling: Logarithmic Spiral is a minimal surface, given by a Weierstrass representation, immersed.
Open Bjorling: Logarithmic Spiral in the interactive viewer →
aperiodic def-weierstrass immersed implemented minimal tradition-classical
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
Bjorling's problem: the unique minimal surface through a given real-analytic strip. The defining seed, reproduced numerically against the shipped row (math_art/minsurf/zoo.py, BJ_LOG_SPIRAL): c(t) = (0.25*cos(t)*exp(0.15*t), 0.25*exp(0.15*t)*sin(t), 0), with normal the Frenet principal normal of the curve, t in [0, 12.56637061]. The Weierstrass data is the holomorphic extension of the seed, computed numerically by the engine -- the seed, not a (g, dh) pair, is what specifies this surface.
Sources
Bjorling seed reproduced numerically against the shipped implementation (math_art/minsurf/zoo.py, row BJ_LOG_SPIRAL): seed reproduced against the shipped callables over 200 samples (worst 0).
- R. Schoen / Lopez & Ros (1991) on the Lopez-Ros deformation; H. F. Scherk (1835) for the base Scherk surface; the decorated-Enneper symmetrization follows M. Weber's repository, https://minimalsurfaces.blog/ (Enneper with n Catenoids).