Fractals and the Fock-Bargmann representation of coherent states
pp. 6-16
in: Peter Bruza, Donald A. Sofge, William F. Lawless (eds), Quantum interaction, Berlin, Springer, 2009Abstract
The self-similarity property of deterministic fractals is studied in the framework of the theory of entire analytical functions. The functional realization of fractals in terms of the q-deformed algebra of coherent states is presented. This sheds some light on the dynamical formation of fractals and provides some insight into the geometrical properties of coherent states. The global nature of fractals appears to emerge from coherent local deformation processes.