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Visualising the Lorenz Manifold

Crochet Lorenz manifold; Osinga & Krauskopf

Crochet Lorenz manifold, closeup; Osinga & Krauskopf

Manifold, view 2; Benjamin Storch

Manifold, view 1; Benjamin Storch

Hinke Osinga and Bernd Krauskopf
Engineering Maths

Benjamin Storch

A steel sculpture, based on one of the most famous objects in chaos theory, has been created by Dr Benjamin Storch, an artist who works with silver and steel. The idea was provided by mathematicians Professor Bernd Krauskopf and Dr Hinke Osinga from the University of Bristol.

Storch turned the maths into art and created a beautiful twisting and winding ribbon of stainless steel. His sculpture Manifold represents a mathematical object known as the Lorenz manifold, a complicated surface that emerges from a famous model of chaotic weather systems. A few years ago, Dr Osinga made a crocheted representation of the same surface, to world-wide acclaim.

It formed the inspiration for the steel sculpture and led to the collaboration between the mathematicians Osinga and Krauskopf and the artist Storch.

“Steel is often associated with large square buildings, but Benjamin’s sculpture seems to float on air,” says Osinga.

“We are absolutely amazed by Benjamin’s craftmanship: Manifold was literally hammered into its intricate shape from flat pieces of steel!” adds Krauskopf.

Storch’s work originates from a desire to create dynamic surfaces in metal. “I am always on the look-out for intriguing imagery in nature and physics,” he says. “My collaboration with Bernd and Hinke is a great example of mathematics and art working hand-in-hand.”

The complex metal-smithing technique that Storch employs, where central surface areas are compressed and peripheral areas are stretched, was perfectly suited for creating Manifold.

Hinke Osinga and Bernd Krauskopf

Dr Hinke Osinga and Professor Bernd Krauskopf have turned the famous Lorenz equations that describe the nature of chaotic systems into a beautiful real-life object, by crocheting computer-generated instructions. Together all the stitches define a complicated surface, called the Lorenz manifold.

The final result consists of 25,511 crochet stitches and took Osinga about 85 hours to complete. However, this wasn't just done for fun. Their work gives insight into how chaos arises and is organised in systems as diverse as chemical reactions, biological networks and even your kitchen mixer.

More about Hinke Osinga

More about Bernd Krauskopf

Benjamin Storch

My interest in sculpture started on a small scale, in the area of jewellery and silversmithing. Very much from the start was I fascinated with both geometric structures and organic designs akin to the 'Art Nouveau' style.

Eventually I found illustrations that combined the organic with the geometric; renderings of fluid, dynamic wave forms that followed simple laws of motion, or their mathematical simulation. This sparked off research into the creation of dynamic surfaces in sheet metal, in connection with mathematical approaches capable of generating the underlying principles.

More recently I have started to take those ideas to a scale suitable for public spaces, where they have a stronger physical presence. What I seek is a tangible sensation of a tensile force field giving rise to contraction, expansion and transformation.

I wouldn't say that the mathematical language is central to my work and ideas, but it has been a useful tool for understanding, applying and sharing some of the mystery surrounding us. While I follow a need to manifest this in solid form, my favourite language is still music and sound.

More about Benjamin Storch.

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