### Hashimoto surfaces

The following images are a space and time discretized Hashimoto or smoke ring flow. You can find the theory behind it here (interactive online version) or here.- the discrete smoke ring flow of a triangle with subdivided edges
- the discrete smoke ring flow of an oval shaped curve

### minimal surfaces

The next three images are s-minimal surfaces: a discretization of minimal surfaces using the notion of discrete s-isothermality. The theory behind it can be found in this article.- a discrete s-minimal catenoid
- a discrete s-minimal Enneper surface
- a discrete s-minimal surface half way in the associated family of the helicoid and catenoid

### cmc surfaces

The next two images show discrete cmc surfaces generated by a discrete version of the DPW mathod. The method is described in*T. Hoffmann. Discrete cmc surfaces and discrete holomorphic maps. In A. Bobenko and R. Seiler, editors, Discrete integrable geometry and physics, pages 97-112. Oxford University Press, 1999.*

- a 6-legged Smyth surface (or Mr Bubble)
- a 3-legged Smyth surface (or Mr Bubble)
- an s-cmc Delaunay surface -- a cmc surface of revolution.

### K-surfaces

- a discrete Kuehn surface. This surface is a Bäcklund transform of the wellknown Pseudosphere. The discretization is described in
*Wunderlich, W.; Zur Differenzengeometrie der Flächen konstanter negativer Krümmung, Sitzungsber. Ak. Wiss., 1951, 160,pages 39-77*and*A. Bobenko and U. Pinkall, Discrete Surfaces with Constant Negative Caussian Curvature and the Hirota Equation, J. Diff. Geom., 1996, 43, pages 527--611.*