TY - JOUR

T1 - Appearance of hierarchical structure in hyper-dilation model

T2 - Model of generalized measurement process

AU - Toyoda, Shin'ichi

AU - Gunji, Pegio Yukio

PY - 1999/9

Y1 - 1999/9

N2 - We show the appearance of emergent hierarchical structure by a generalized system based on hyper-dilation (P.-Y. Gunji, S. Toyoda, Biosystem 38 (1996) 127-133), that is a new approach for complex systems. Hyper-dilation comprises a measurement problem hidden in any formal system. In hyper-dilation, the measurement process is expressed as the interface between an infinite lattice, which is an infinite loop of a rule, and a finite lattice, which is a tree structure of a rule. Hyper-dilation shows two intrinsic properties, one is degeneracy of a Cantor set in return map, and the other is generation of 1/f noise. We present various versions of hyper-dilation and suggest that to generate 1/f noise, it is required that the rules of the system are changed through a coherent process and that the system is closed for information. From these two properties of hyper-dilation, we discuss that the degeneracy is regarded as the model of emergence of a new hierarchy, and in hyper-dilation, actually we show the motion of a system that can be regarded as the appearance of a new hierarchy.

AB - We show the appearance of emergent hierarchical structure by a generalized system based on hyper-dilation (P.-Y. Gunji, S. Toyoda, Biosystem 38 (1996) 127-133), that is a new approach for complex systems. Hyper-dilation comprises a measurement problem hidden in any formal system. In hyper-dilation, the measurement process is expressed as the interface between an infinite lattice, which is an infinite loop of a rule, and a finite lattice, which is a tree structure of a rule. Hyper-dilation shows two intrinsic properties, one is degeneracy of a Cantor set in return map, and the other is generation of 1/f noise. We present various versions of hyper-dilation and suggest that to generate 1/f noise, it is required that the rules of the system are changed through a coherent process and that the system is closed for information. From these two properties of hyper-dilation, we discuss that the degeneracy is regarded as the model of emergence of a new hierarchy, and in hyper-dilation, actually we show the motion of a system that can be regarded as the appearance of a new hierarchy.

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U2 - 10.1016/S0096-3003(98)10063-2

DO - 10.1016/S0096-3003(98)10063-2

M3 - Article

AN - SCOPUS:0347596681

VL - 104

SP - 153

EP - 178

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

SN - 0096-3003

IS - 2-3

ER -