Kostya has started to estimate the fractal dimension of the electron / pion showers in DIF plane.
This method was first proposed by Manqi Ruan and published in Phys. Rev. Lett. 112, 012001, arXiv:1312.7662 [physics.ins-det].

Kostya used 3 different definitions of fractal dimensions, the third one is similar to the original Manqi's proposal (though, ln = log_e was used instead of log_2), projected in 2-dimensional plane.
What can be studied further is a dependence of the fractal dimension on the energy cut.

The MC GEANT4 simulation is already well advanced, the codes are available in
https://github.com/apsallid/SiWEcal