Are neurons multifractals?

In the last few years, fractal analysis has found widespread application in the field of neuroscience and some investigators are starting to use multifractals as a methodology that may provide information about the distribution of fractal dimensions in biological structures. This is so, despite of the technical difficulties of multifractal analysis. In this paper, we investigate the theoretical and practical aspects of studying and measuring the multifractal dimensions of neurons. Patterns were analysed by means of the standard box-counting method and a generalised sand-box method. Our results show that odd behaviours of Dq reported in the literature are a consequence of numerical deficiencies of the box-counting method and cannot be associated to peculiar geometrical characteristics of neurons. Instead the sand-box method gives a Dq which monotonically decreases with q. Although this result may indicate that neurons are multifractals, it is argued that size effects may in fact be the origin of this apparent multifractality.