### Fractal Dimension

The **Fractal Dimension** model measures the complexity of a 2-dimensional structure by calculating its box-counting dimension [25]. The idea is to subdivide the area into a number of square boxes and simply count the number of boxes containing some part of the structure. The mesh size is defined as s, so 1/s gives the number of segments in each of the 2 dimensions. Specifying 1/s=5 therefore means a subdivision into 5*5=25 boxes. This counting process is repeated with increasing the number of intervals to a specified maximum number given as a model parameter. Next, the data are plotted in a double-logarithmic way, namely log(N(s)) on the y axis and log(1/s) on the x-axis. The box-counting dimension is then obtained as the slope of a linear regression through the plotted points.

We would like to thank Prof. Ludwig G. Strauss (l.strauss@dkfz-heidelberg.de) for the model implementation and for making it publicly available.