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Home > Crocheted Lorenz Manifolds
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"Crocheted Lorenz manifold, black background," by Hinke Osinga, in collaboration with Bernd Krauskopf, Department of Engineering Mathematics, University of Bristol (

Dr. Hinke Osinga and Professor Bernd Krauskopf (Engineering Mathematics, University of Bristol) have 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.

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.

For more information, the crochet pattern and mounting instructions, see:

hinke-crochet-detail.jpg hinke-crochet-white~0.jpg hinke-crochet-black.jpg

American Mathematical Society