Propagation through fractal media: The Sierpinski gasket and the Koch curve

¹ Grup de Física Estadística, Departament de Física Universitat Autònoma de Barcelona - E-08193 Bellaterra, Barcelona, Spain
² Departament de Física, Universitat de Girona Campus Montilivi, E-17071 Girona, Spain
³ Departament de Medicina, Facultat de Ciències de la Salut Universitat Internacional de Catalunya - c./Josep Trueta s/n E-08190 Sant Cugat del Vallès, Barcelona, Spain

Received: 7 April 2004
Accepted: 18 October 2004

Abstract

We present new analytical tools able to predict the averaged behavior of fronts spreading through self-similar spatial systems starting from reaction-diffusion equations. The averaged speed for these fronts is predicted and compared with the predictions from a more general equation (proposed in a previous work of ours) and simulations. We focus here on two fractals, the Sierpinski gasket (SG) and the Koch curve (KC), for two reasons, i.e. i) they are widely known structures and ii) they are deterministic fractals, so the analytical study of them turns out to be more intuitive. These structures, despite their simplicity, let us observe several characteristics of fractal fronts. Finally, we discuss the usefulness and limitations of our approach.