The Hofstadter butterfly spectrum for Landau levels in a two-dimensional periodic lattice is a rare example exhibiting fractal properties in a truly quantum system. However, the observation of this physical phenomenon in a conventional material will require a magnetic field strength several orders of magnitude larger than what can be produced in a modern laboratory. It turns out that for a spec...

1.1. Statement of the results. In this note we analyze simple models of classical chaotic open systems and of their quantizations. They provide a numerical confirmation of the fractal Weyl law for the density of quantum resonances of such systems. The exponent in that law is related to the dimension of the classical repeller of the system. In a simplified model, a rigorous argument gives the fu...

The inner knowledge of volumes from images is an ancient problem. This question becomes complicated when it concerns quantization, as the case of any measurement and in particular the calculation of fractal dimensions. Trabecular bone tissues have, like many natural elements, an architecture which shows a fractal aspect. Many studies have already been developed according to this approach. The q...

The similarity in fractal dimensions of paint “blobs” in samples of gestural expressionist art implies that these pigment structures are statistically indistinguishable from one another. This result suggests that such dimensions cannot be used as a “fingerprint” for identifying the work of a single artist. To overcome this limitation, the multifractal spectrum is adopted as an alternative tool ...

A hybrid 3D compression scheme which combines fractal coding with neighbourhood vector quantisation for video and volume data is reported. While fractal coding exploits the redundancy present in different scales, neighbourhood vector quantisation, as a generalisation of translational motion compensation, is a useful method for removing both intraand interframe coherences. The hybrid coder outpe...