What do you yet when you cross a rubber band with an octopus? A whole new shape, it turns out, with perversions.

The Harvard researchers who made the discovery were seeking to make springs. They glued two strips of uneven length together and stretched them out while clipped at each end with strings thin enough that the strips could rotate freely. As the force stretching the strips out decreased the strips started to wind up like a telephone cord (ask someone over 30).

While the new shape resembles a double helix the team noticed it had what they call perversions (see image above). Technically it is a hemihelix, a sort of helix that shifts from spiraling in a clockwise direction to an anticlockwise one, or vice versa. A change in direction is called a perversion . Darwin observed what we now call perversions in the tendrils of climbing plants that gain purchase on another object.

What was unexpected was that the bands developed not just one perversion, but as many as eleven. In PloS ONE the team demonstrate that “the number of perversions depends on the height to width ratio of the strip's cross-section.” Strips that are wide enough relative to their height turned into helices, that is had no perversions at all. Those with small height to width rations produced many perversions. The authors add “Our findings provide the basis for the deterministic manufacture of a variety of complex three-dimensional shapes from flat strips.”

"Once you are able to fabricate these complex shapes and control them, the next step will be to see if they have unusual properties; for example, to look at their effect on the propagation of light," says Associate Professor Katia Bertoldi, one of the authors.

Helices and hemihelices are common in nature. “Initially straight roots form helical shapes while attempting to penetrate more compact soils ,” the paper notes. The authors suspect the reason the behavior has not been observed before is that most materials would snap under the pressures endured in this case. Perversions have an elastic energy that causes them to repel each other and therefore adopt a regular order to avoid getting too close.

"We see deterministic growth from a two-dimensional state—two strips bonded together—to a three-dimensional state," says lead author Jia Liu. "The actual number of perversions, the diameter, everything else about it is entirely prescribed. There is no randomness; it's fully deterministic. So if you make one hundred of these, they'll always perform exactly the same way." This could prove useful in replicating complex shapes seen in nature.

The formation of perversions represented something of a puzzle, since a helix is the energetically lowest possible system. However, mode instabilities can prevent the formation of a helix and where the width to height ration is suitable the authors note strings can be “trapped in higher energy states and only removed by the application of an external set of forces”.

And the octopus? The team originally came up with the experiment trying to make new springs inspired by cephalopods, the class of molluscs that includes octopi, squids, cuttlefish and nautilus.