We developed an alternative index so called ht-index (Jiang and Yin 2014), alternative to fractal dimension, for characterizing the complexity of fractals or fractal patterns. We have also relaxed the definition of fractals (Jiang 2015), i.e., a set or pattern is fractal if and only if there are far more small things than large ones.
Jiang B. and Yin J. (2014), Ht-index for quantifying the fractal or scaling structure of geographic features, Annals of the Association of American Geographers, 104(3), 530–541.
Jiang B. (2015), Head/tail breaks for visualization of city structure and dynamics, Cities, 43, 69-77.