A study on complexity measures

• Main Author: Andri Pradana
• Other Authors: Chew Lock Yue
• Format: Final Year Project
• Language: English
• Published: 2013
• Subjects: DRNTU::Science::Physics
• Online Access: http://hdl.handle.net/10356/53676
• Institution: Nanyang Technological University

In this study, we develop a technique to measure randomness and complexity for various systems. The measures were applied to different systems: the pseudo-random number generators (C-native rand() & lrand48(), and the Mersenne twister algorithm), the arc-fractal system, and the Abelian Manna sandpile model (AMM). The aim was to reveal, to some extent, the internal structure of these systems. For the pseudo-random number generators, we found that the sequences from C-native rand() and Mersenne twister algorithm were sufficiently random, while some of the sequences from the C-native lrand48() were less random. The complexity measure revealed that there was imperfectness in the statistical distribution of these lrand48() sequences. It showed the lrand48() might be sensitive to modulus operation. The seemingly random sequences representing the arc-fractals were found to have very low degree of randomness. There are patterns in the sequences that conform to the structure of the pattern in the arc-fractals. Furthermore, we also found that the Out-In-Out (Crab) and In-Out-In (Arrowhead) construction rules were complementary to each other. The measures also revealed the dynamics of activities of particles in one-dimensional chain lattice and two-dimensional square lattice AMM. Higher activity of particles were observed when the entrance and exit of particles were constrained to fixed sites, while lower activity was observed when they were spread out to many sites on the lattice. Furthermore, there is a linear randomness-complexity relationship in AMM.