Stability analysis of cellular automata generated clusters

Abstract

The development of regional urban system still remains one of the main problems during the human race history. There are a lot of problems inside this system like overcrowded cities and decaying countryside. All these situations can be reproduced by modelling them using Cellular Automata (CA) [1, 2, 5]. CA models implement algorithms with simple rules and parameter controls, but the result can be a complex behaviour.

A stability of naturally formed self‐organized urban system depends on its critical state parameter τ in the power law log(f(x)) = ‐τlog(x). If the system reaches self‐organized critical (SOC) state then it remains in it for a long time. The CA model URBACAM (URBAnistic Cellular Automata Model) describes the long‐lasting term behaviour and shows that the change in behaviour is sensitive to the urban parameter τ of the power law.

Regionines urbanistines sistemos vystymasis išlieka viena iš opiausiu problemu žmonijos istorijoje. Keletas tokiu uždaviniu kaip miestu perpildymas, nykstančios kaimo vietoves ir t.t. gali būti nesunkiai modeliuojami naudojant lasteliu automatus (LA). LA metodas ypatingas tuo, kad realizuoja algoritma paprastu taisykliu bei parametru valdymo pagalba, tačiau rezultate galima gauti sudetinga elgsena. Natūraliai susiformavusiu urbanistiniu sistemu stabilumas priklauso nuo sistemos krizines savirangos būsenos (KSB) parametro τ. Jei sistema pasiekia KSB, tai ji ilga laika išlieka joje. LA modelis URBACAM charakterizuoja ilgalaike elgsena ir parodo, jog modelyje jos kitimus itakoja eksponentinio desnio urbanistinis parametras τ.

Key words:

• cellular automata
• clustering
• urban growth
• stability analysis