TY - JOUR

T1 - Dynamics of extended Schelling models

AU - Vieira, André P.

AU - Goles, Eric

AU - Herrmann, Hans J.

N1 - Publisher Copyright:
© 2020 IOP Publishing Ltd and SISSA Medialab srl.

PY - 2020

Y1 - 2020

N2 - We explore extensions of Schelling's model of social dynamics, in which two types of agents live on a checkerboard lattice and move in order to optimize their own satisfaction, which depends on how many agents among their neighbors are of their same type. For each number n of same-type nearest neighbors we independently assign a binary satisfaction variable s k which is equal to one only if the agent is satisfied with that condition, and is equal to zero otherwise. This defines 32 different satisfaction rules, which we investigate in detail, focusing on pattern formation and measuring segregation with the help of an 'energy' function which is related to the number of neighboring agents of different types and plays no role in the dynamics. We consider the checkerboard lattice to be fully occupied and the dynamics consist of switching the locations of randomly selected unsatisfied agents of opposite types. We show that, starting from a random distribution of agents, only a small number of rules lead to (nearly) fully segregated patterns in the long run, with many rules leading to chaotic steady-state behavior. Nevertheless, other interesting patterns may also be dynamically generated, such as 'anti-segregated' patterns as well as patterns resembling sponges.

AB - We explore extensions of Schelling's model of social dynamics, in which two types of agents live on a checkerboard lattice and move in order to optimize their own satisfaction, which depends on how many agents among their neighbors are of their same type. For each number n of same-type nearest neighbors we independently assign a binary satisfaction variable s k which is equal to one only if the agent is satisfied with that condition, and is equal to zero otherwise. This defines 32 different satisfaction rules, which we investigate in detail, focusing on pattern formation and measuring segregation with the help of an 'energy' function which is related to the number of neighboring agents of different types and plays no role in the dynamics. We consider the checkerboard lattice to be fully occupied and the dynamics consist of switching the locations of randomly selected unsatisfied agents of opposite types. We show that, starting from a random distribution of agents, only a small number of rules lead to (nearly) fully segregated patterns in the long run, with many rules leading to chaotic steady-state behavior. Nevertheless, other interesting patterns may also be dynamically generated, such as 'anti-segregated' patterns as well as patterns resembling sponges.

KW - absorbing states

KW - cellular automata

KW - dynamical processes

KW - stationary states

UR - http://www.scopus.com/inward/record.url?scp=85082422985&partnerID=8YFLogxK

U2 - 10.1088/1742-5468/ab5b8d

DO - 10.1088/1742-5468/ab5b8d

M3 - Article

AN - SCOPUS:85082422985

VL - 2020

JO - Journal of Statistical Mechanics: Theory and Experiment

JF - Journal of Statistical Mechanics: Theory and Experiment

SN - 1742-5468

IS - 1

M1 - 013212

ER -