Here is an image showing how DLA-based fractal model changes when couple of density parameters are slightly tilted. The whole thing is here to generate a fractal probability distribution for geographical Yook/Jeong/Barabasi network model.
Maybe IFS-based fractal would be better here - as it might allow for more control of fractal dimension than DLA does. But then I would not get an obvious way to control exponential density fall-off, and IFS seems to be less natural than this DLA.
Also, here're some resources on fractal generation I'd stumbled upon recently:
- Larry Riddle's Classic Iterated Function Systems - quite thorough in-depth survey of several well-known fractals;
- E. Garcia's Fractal Clusters/Networks page - featuring side-by-side comparison of different fractal network formations;
- Fractals Page at Math Archives Project - lots of related resources;
- Andy Lomas's Pictures of Aggregation - quite remarkable 3-dimensional fractal art;