It can be used to model a whole range of natural phenomena and in certain circumstances fractal dimension estimates can be linked to various other properties of the object or process under investigation.
Fractal geometry has a lot to offer the engineering community.
This page summarises four research projects of Dr. Addison which use techniques from fractal geometry in engineering research studies. This has caused a massive loss in resolution, so I've zipped up all the original full-sized versions and you can download them if you wish. A non-Fickian diffusion model is being developed using techniques from fractal geometry. The figure below shows the time evolution of two diffusing clouds, released in a coastal bay area. Both have the same diffusion coefficient.