Detecting structural complexity: From visiometrics to genomics and brain research

From visual inspection of complex phenomena to modern visiometrics, the quest for relating aspects of structural and morphological complexity to hidden physical and biological laws has accompanied progress in science ever since its origin. By using concepts and methods borrowed from differential and integral geometry, geometric and algebraic topology, and information from dynamical system analysis, there is now an unprecedented chance to develop new powerful diagnostic tools to detect and analyze complexity from both observational and computational data, relating this complexity to fundamental properties of the system. In this paper we briefly review some of the most recent developments and results in the field. We give some examples, taken from studies on vortex entanglement, topological complexity of magnetic fields, DNA knots, by concluding with some comments on morphological analysis of structures present as far afield as in cosmology and brain research. © Springer-Verlag Italia, Milano 2009.