Yanguang Chen
Department of Geography
College of Urban and Environmental Sciences,
Peking University, Beijing 100871, PR China

ArXiv: Spatial Dynamics of Urban Growth Based on Entropy and Fractal Dimension
Homepage
Key Quote:  “This suggests that the origin of bifurcation and chaos is two-population coupling and interaction rather than intrinsic randomicity of determinate models.”

First email: 21 April 2018

Dear Prof. Dr. Yanguang Chen:

Reading your ArXiv papers, particularly Reinterpreting the Origin of Bifurcation and Chaos by Urbanization Dynamics (2017), whereby “the 2-dimensional rural-urban coupling map can create the same bifurcation and chaos patterns as those from the 1-dimensional logistic map.”

I wonder if you might think about a very interesting progression created by doubling the Planck base units, then doubling each new value. Once doubled 202 times, Planck Time has gone from the first moment of time to this very day: https://81018.com/chart

It would seem such a progression opens more questions than answers, yet it embraces chaos,  I believe, in a more fundamental manner than the urbanization measurement and this progression calls to question the conclusion that “the whole trajectory expands infinitely in the region between two radicals. ”

May I call you for a discussion?

Thank you.

Most sincerely,
Bruce
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Bruce Camber
http://81018.com
Bifurcation/chaos homepage: https://81018.com/imagination