Fractal Properties of Linux Kernel Maps

Abstract

Many different measures were proposed to describe the problem of possible software complexity - the number of lines of code sometimes referred as a source lines of code (SLOC), Halstead’s volume V, McCabe cyclomatic number V(G), among others. However, any of them doesn’t take into account the possible fractal properties of software source code emerging from development process. The main aim of this paper is to show that in the case of successive Linux OS kernels fractal self-organization of the system can be seen. This is done in the relation to: (i) the analysis of rate of growth for number of files and source lines of Linux kernels code, (ii) by the presentation of some visualizations indicating self-similar graphical structure of OS kernels, (iii) by the calculations of fractal dimensions Db basing on box dimension method. Basing on obtained results it can be assumed that: (i) calculated rate of growth in the case of lines and files in the simplest approach can be approximated by the polynomial with degree 2 with R = 0.96 and R = 0.94 respectively, (ii) this system becomes more and more complex with self-similar structure, (iii) its fractal dimension is still growing. Presented analysis opens new possibilities for description of computer programs in terms of complex systems approach.