Geography in motion: Hexagonal spatial systems in fuzzy gravitation

Abstract

The dynamics of spatial hierarchical processes displays fascinating images of the evolution of attraction basins of towns. Assuming in the present paper a random character of such complex processes, gravitational modeling is employed to depict changes in the nature of fuzzy boundaries between attraction basins in a hexagonal world, i.e. the geographical pattern central in the renowned and influential Christaller–Lösch central place theory in geography. The paper presents various interesting stylized maps of such stochastic processes. Our findings demonstrate that the collective behavior of actors in geographic space shows a white noise pattern that mirrors a fuzzy gravitation towards large population concentrations. These results support the validity of the conventional central place theory.

Fractal Dimension Complexity of Gravitation Fractals in Central Place Theory

“…Our research conducted here also confirms the conclusions presented in previous works by Banaszak et al (2015Banaszak et al ( , 2019 concerning the transformation of chaos into spatial order, which means the stabilization of permanent dominance, usually of one attractor (city). Thus, with regard to fragments A and D, in fragment A there is a constant dominance (in half of the area) of cities 1 and 6, from the limit value of μ = 0.24 onward.…”

“…Conducted in the spirit of recent works by Banaszak et al, (2015Banaszak et al, ( , 2019, this study is devoted to the dynamics of spatial interactions generated by urban units included in a regular hexagonal CPT pattern (see also : Allen, 1997;Allen and Sanglier, 1979;Allen, Sanglier, 1981;Alligood et al, 1996;Bandt and Mekhontsev, 2018;Chen, 2011;Dzięcielski et al, 2021;Fujita et al 2001;Ikeda et al, 2014Ikeda et al, , 2017Letellier et al, 2021;White, 1977). It seeks to develop a comprehensive dynamic 'umbrella' methodology in which prevailing static CPT approaches can be positioned and combined from a unitary Newtonian motion perspective on hierarchical systems.…”

Regional science in the Netherlands: A contextual interpretation of the “power of smallness”

“…Further contributions to the analysis of spatially interdependent hierarchical systems, called Tinbergen‐Bos systems, were undertaken by Paelinck and others (see, e.g., Griffith & Paelinck, ; Kuiper, Kuiper, & Paelinck, ). Another recent example of a dynamic modelling study on the complex, fractal and sometimes chaotic nature of central place systems can be found in Banaszak, Dziecielski, Nijkamp, and Ratacjak (, ).…”