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Tim Hoffmann

Tim Hoffmann [an error occurred while processing this directive] math picture gallery

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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.
smoke ring 1
the discrete smoke ring flow of a triangle with subdivided edges
smoke ring 2
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.
catenoid
a discrete s-minimal catenoid
enneper's surface
a discrete s-minimal Enneper surface
in the associated family of the catenoid
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.
Smyth surface 6-legged
a 6-legged Smyth surface (or Mr Bubble)
Smyth surface 3-legged
a 3-legged Smyth surface (or Mr Bubble)
s-cmc Delaunay
an s-cmc Delaunay surface -- a cmc surface of revolution.

K-surfaces

Kuehn's surface
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.

other

spin transform of the cylinder
a spin transform of the s-isothermic cylinder
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