### Building with fractals: when more means less

Researchers are designing ultralight structures using fractal patterns and demonstrating that these fractal architectures require a lot less material to retain the mechanical strength of their non-fractal progenitors.

Fractal patterns can be used to describe everything from the tree branches and snowflakes, the structure of the Eiffel tower, the amyloid proteins associated with Alzheimer's disease, to Jackson Pollock's drip paintings

A fractal describes a "self-similar" pattern, whose component parts have a structure similar to the structure they create-- like a fern frond that's made up of little fronds.
 Image Credit: Ian Britton

British mathematician Michael Barnsley was the first person to show that the fern structure could be described by a mathematically repeating pattern.

 Barnsley Fern. Image Credit: Mike Borrello
In the new paper in the journal Physics Review Letters, scientists use theoretical calculations to show that a structure comprised of a more complex fractal pattern requires less material to support a load than a structure without a fractal pattern. The authors of the paper are Yong Mao and Daniel Rayneau-Kirkhope, at the University of Nottingham, UK, and Robert Farr, from the London School of Mathematical Sciences, UK.

The "order" of the structure reflects the hierarchy, or the number of times the pattern has repeated. In this example, the scientists consider a hollow rod to be the 0th-order structure, and call the 1st-order structure the triangle frame seen in (a). The next level up, the 2nd-order structure, rebuilds the structure replacing the simple rods with the the 1st-order structure as the basic unit. The 2nd-order structure is shown in (b). A 3rd-order structure would replace each triangle leg with rods of the 2nd-order structure, (b). And so on, and so forth.

 D.Rayneau-Kirkhope et al.Ultralight fractal structures from hollow tubes. Physics Review Letters 2012.
The 2nd-order structure (b) requires less material than the simpler 1st-order structure (a), but they can both bear the same weight.

This has serious consequences when it's scaled up, the researchers propose. For instance, the team calculates that a 200-meter long beam carrying 1000 kg (about the mass of a dairy cow) would require 79 tons of steel. A beam built out of a 3rd-order structure would only require 162kg (a mass of about 2 people). The 3rd-order beam would be 500 times lighter than in the solid beam.

The scientists anticipate that fractal-based design will advance the development of lightweight materials, particularly as scientists start to build with the smallest kind of rods -- carbon nanotubes -- and as new methods of fabrication make it easier to build large-scale structures with geometric patterns -- as with 3D printed airplanes.

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1. The rendering time will become a significant factor in using ths as a construction method. Currently, flow assembly processes are used in nano technologies allowing the substrates to become the templates. To create even a 2nd order spar requires some serious electrochemical laser manufacturing on the industrial silicon scale.

The biological systems still form the best technology for manufacturing such structures, and that is where research ought to be directed. The carbon footprint of any other technology would be enormous!

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### The Science of Ice Cream: Part One

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