We introduce a class of dynamical systems called Higher Order Cellular Automata (HOCA). These are based on ordinary CA, but have a hierarchical, or multi-level, structure and/or dynamics. We present a detailed formalism for HOCA and illustrate the concepts through four examples. Throughout the article we emphasize the principles and ideas behind the construction of HOCA, such that these easily can be applied to other types of dynamical systems. The article also presents new concepts and ideas for describing and studying hierarchial dynamics in general.
AbstractEroders are monotonic cellular automata with a linearly ordered state set that eventually wipe out any finite island of nonzero states. One-dimensional eroders were studied by Gal’perin in the 1970s, who presented a simple combinatorial characterization of the class. The multi-dimensional case has been studied by Toom and others, but no such characterization has been found. We prove a similar characterization for those one-dimensional monotonic cellular automata that are eroders even in the presence of random noise.
This paper proposes a digital watermarking method for the protection of medical volume data based on chaotic neural network and 3D DWT-DFT. In order to improve the security of digital watermarking, it uses chaotic sequence for scrambling .The chaotic sequence is generated by chaotic neural network. It makes full use of multi-level decomposition characteristics of 3D DWT-DFT, embedding watermark in the transform domain. The experimental results show that the method can resist filtering and rotation attacks, which has good robustness.
Stable Multi-Level Monotonic Eroders