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We explore the fractal nature of particle showers using Monte-Carlosimulation. We define the fractal dimension of showers measured in a highgranularity calorimeter designed for a future lepton collider. The showerfractal dimension reveals detailed information of the spatial configuration ofthe shower. %the information hidden in the details of shower spatialconfiguration, It is found to be characteristic of the type of interaction andhighly sensitive to the nature of the incident particle. Using the showerfractal dimension, we demonstrate a particle identification algorithm that canefficiently separate electromagnetic showers, hadronic showers andnon-showering tracks. We also find a logarithmic dependence of the showerfractal dimension on the particle energy.

Fractal Dimension of Particle Showers Measured in a Highly Granular Calorimeter