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/vol03/zheng/ | © Copyright 1996 | |||
| Volume 03 | Received: Accepted: |
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Conjugate Visualisation of Global Complex Behaviour
Zhi J. Zheng |
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| Abstract | |
| 2D maps (Poincare maps) play a key role in representing global behavior of complex dynamic systems under continuous and partially continuous conditions. Binary image sequences have discrete time, space and state. Discrete conditions create severe difficulties in applying 2D map techniques to visualising complex dynamic behaviour of the image sequences. In [13], [12], [11] four statistical measures are proposed for constructing 2D maps to represent complex dynamic behaviour of binary image sequences. It is possible to use the four statistical measure sequences by analogy to construct four Poincare maps (for serial measures) and two additional maps, conjugate maps (for parallel measures). A 2D conjugate map generated by two statistical measures of the variations is distributed in a triangular area. Similar to Poincare maps, the new map represents different complex dynamic behaviour of image sequences as respective trajectories. In this paper, investigations are focused on exploring complement properties for pairs of chaotic rules of 1D cellular automata (k=2, r=1). It can be shown that if two chaotic rules satisfy the pair of 0-1 complement, then their trajectories will have reflection symmetry in conjugate maps. This new map provides additional information in visualising complex dynamic behaviour of chaotic image sequences using the conjugate representations. | |
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