If Benoît Mandelbrot, who died in October, was sometimes pugnacious and fiercely protective of his priority claims, that's often how it is with scientists whose ideas genuinely alter science. Although some of the concepts underpinning fractal geometry did not originate with Mandelbrot, he saw their significance (and gave fractals their name), and his strong advocacy established the notion of self-similarity in topics ranging from economics to geomorphology and developmental biology.

At its most reductive level, Mandelbrot's message was that shape can matter: although a metal behaves the same way if it is a sphere or a cube, it may not do so when it has a fractal geometry. This notion is underscored in a report by Rémi Carminati and co-workers in Paris of localization of electromagnetic waves in a fractal gold film1.

This sort of localization, in which a wave cannot propagate through a disordered medium because of strong scattering, was predicted by Philip Anderson, who showed that if a semiconductor contains a high proportion of randomly distributed defects such as impurities, interference between multiply scattered electron waves can prevent their diffusion, leading to insulating behaviour2.

This is a general phenomenon of waves, applying equally to the propagation of sound and light. And indeed, the localization of light was reported in 1997 in powdered gallium arsenide3. In general, the degree of localization of the light field ought to be governed by the diffraction limit, so that the bright or 'hot' spots cannot be smaller than half a wavelength. However, that restriction for electromagnetic waves is relaxed in the system studied by Carminati et al., because the optical energy is carried in surface plasmons: coherent excitations of electrons on (in this case) metal surfaces. It is for this reason that plasmonic excitations can convey light through holes in metal films smaller than the half-wavelength limit4.

When such metal films are strongly inhomogeneous — if, for example, they are composed of fractal aggregates of nanoparticles — it was predicted that the plasmonic field should exhibit strong Anderson localization5. What's more, the fractal geometry of such a system imposes a unique signature on the localization, which is (like the fractal clusters themselves) scale-free: the hot spots exist on all size scales ranging from those of the nanoscale components of the system to that of the entire cluster. And the size of the hot spots should fluctuate widely from one cluster to another.

This is what Carminati et al. have observed1,6. They use fluorescent polystyrene beads to probe the optical states in thin films made from gold nanoparticles aggregated into reticulated, fractal networks. The fluorescence decay rates of the probe particles reveal large, scale-free fluctuations in the local density of optical states, as predicted theoretically.

This curious system is of more than academic interest. Random thin films such as this enhance Raman scattering from objects on their surface, a characteristic used for the sensitive detection of chemical and biological substances. That enhancement is related to the film's optical properties, which can now be understood as a product of their fractal geometry.