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Mathematical ImageryMathematicians and artists create strong, stunning, works in all media and explore the visualization of mathematics


Crocheted Lorenz Manifolds :: Hinke Osinga & Bernd Krauskopf

Dr. Hinke Osinga and Professor Bernd Krauskopf (University of Auckland) turned the famous Lorenz equations into a beautiful real-life object, by crocheting computer-generated instructions of the Lorenz manifold: all crochet stitches together define the surface of initial conditions that under influence of the vector field generated by the Lorenz equations end up at the origin; all other initial conditions go to the butterfly attractor that has chaotic dynamics.

Crocheted Lorenz manifold, black background

The black background in the photograph brings out the separating properties of the Lorenz manifold: points on one side of the surface can never cross to the other side, even though they will visit both left and right wings of the butterfly attractor in a seemingly unpredictable manner.

Crocheted Lorenz manifold, white background

The white background in the photograph brings out the rotational symmetry of the Lorenz manifold and gives an idea of the structure of the mesh.

Hinke crochet - detail

The photograph shows a particularly nice detail of the intriguing geometry of the Lorenz manifold. The wire running through the crocheted work illustrates one of the paths on the surface that end at the origin.