fish sculpture

Engineers use fractals to mimic ‘metallic’ fish skin

The shiny skins of certain ribbonfish reflect light across a broad range of wavelengths, giving them a brilliant metallic appearance.

The reflectivity is the result of stacked layers of crystalline organic compounds embedded in their skin’s cytoplasm. Some organisms with metallic sheens have layers that are stacked in a regular pattern, while others, including the ribbonfish, have stacking patterns described as “chaotic” or random.

Researchers determined that the stacking is not completely random and developed mathematical algorithms to replicate those patterns in semiconductor materials.

“We are proposing a model that uses fractal geometry to describe the layering in the biological structure of silvery fish,” says Jeremy Bossard, postdoctoral researcher in electrical engineering at Penn State. “While we are not trying to reproduce the structure found in nature, the same model could guide the design of devices such as broadband mirrors.”

[Zoom in on metallic glasses to find fractals]

Fractals have been called the “geometry of nature” because they can help describe the irregular but self-similar patterns that occur in natural objects such as branching tree limbs.

The researchers use a one-dimensional fractal, known as a Cantor bar fractal, which is a line divided by spaces or gaps. Normally, Cantor fractals appear to be very regular, but when random changes are introduced to the geometry, a more complex pattern emerges. The pattern resembles the layering of reflective layers in ribbonfish skin.

“There is an underlying pattern, but there is randomness built in,” says Bossard, “similar to the way that living trees have an overall fractal pattern but do not grow symmetrically.”

[Skin lets these fish do a vanishing act]

The researchers then use another nature-inspired computational method called a genetic algorithm that mimics Darwinian evolution to create successive generations of fractal patterns from the parent patterns. Over approximately 100 generations, the patterns converge on the best design to meet all the target requirements.

Using fractals and the genetic algorithm, the researchers were able to mathematically generate patterns targeting optical functions in the mid-infrared and near-infrared ranges, including broadband reflection.

They propose that the design approach could be used to develop nanoscale stacks with customized reflective spectra. The research results are reported in the Journal of the Royal Society Interface.

The National Science Foundation’s Center for Nanoscale Science and Penn State supported the work.

Source: Penn State