Appearance of hierarchical structure in hyper-dilation model: Model of generalized measurement process

Shin'ichi Toyoda*, Pegio Yukio Gunji

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)153-178
Number of pages26
JournalApplied Mathematics and Computation
Issue number2-3
Publication statusPublished - 1999 Sep
Externally publishedYes

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics


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