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Fractal properties of Linux self-organized kernel maps

Dominik Strzałka 

Rzeszow University of Technology, Rzeszów, Poland

Abstract

Many different measures were proposed to describe the problem of possible software complexity. Among them there are: the number of lines of code sometimes reffered as source lines of code (SLOC), Halstead’s volume V, McCabe cyclomatic number V(G), etc. However, any of them don’t take into account the possible fractal properties of software code developement.

One of the most popular measures of software complexity is the number of source lines of code (SLOC). This measure gives the size of software program by counting the number of lines in the text of program’s source code. It helps to predict the amount of effort that will be required to develop the program. Usually this number is big and it can even achieve 107 lines. However, this measure has got many disadvantages, for example the lack of accountability, the lack of counting standards, the problems with multiple languages, etc. Bill Gates said that: “Measuring programming progress by lines of code is like measuring aircraft building progress by weight”. Despite that, this quantity is quite often given, because it can help imagine how dificult was the developement of software and how this software is “big”.

A self-organiation is one of the most amazing properties in the case of many complex systems. It can be considered as a process in which the internal organization of a system (usually it’s an open system), increases in complexity without management by an outside source.  Systems that self-organize typically display many emergent properties.

In the case of mathematics and computer science this phenomenon is usually connected with the ideas of cellular automata, graphs (especially in complex networks like "small worlds" and scale-free networks), and some instances of evolutionary computation and artificial life. In the field of multi-agent systems a very active research area is the problem how to engineer such systems that will be capable of presenting the self-organized behavior. In this paper we will show that there are also other fields where the self-organization can appear. Such a field is the cooperation (maybe sometimes independent) of many programmers that leads to the developement of software.

The paper will show the property of system self-organization in the case of succesive Linux OS kernels. The presented visualisations will indicate how the OS kernels can be complex through their self-similar structure. The succesive Linux kernel distributions are commonly used operating systems that are developed and tested by many enthusiasts. For each stable Linux kernel visualization there will be also calculated the fractal dimension basing on box dimension method.

 

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Related papers

Presentation: Poster at 5 Ogólnopolskie Sympozjum "Fizyka w Ekonomii i Naukach Społecznych", by Dominik Strzałka
See On-line Journal of 5 Ogólnopolskie Sympozjum "Fizyka w Ekonomii i Naukach Społecznych"

Submitted: 2010-09-15 13:58
Revised:   2010-09-16 09:49