# Paradox of integration---Cellular automata approach

## TL;DR

This paper reformulates a social integration model using cellular automata, demonstrating that the self-deprecating strategy effectively reduces conflict by balancing real and surface statuses, consistent with previous differential equation results.

## Contribution

It introduces a cellular automata approach to model social integration, providing a new probabilistic framework that confirms earlier findings from differential equations.

## Key findings

- Cellular automata replicate previous differential equation results.
- Surface status enhancement balances real status deficiencies.
- Both synchronous and asynchronous automata yield similar outcomes.

## Abstract

We discuss the self-deprecating strategy introduced by Peter Blau as one of stages of the process of social integration. Recently we have introduced a two-dimensional space of status, real and surface one ($A$ and $B$), and we have demonstrated that with this setup, the self-deprecating strategy efficiently prevents the rejection [K. Malarz and K. Kulakowski, International Journal of Modern Physics C 30, 1950040 (2019)]. There, the process of reducing the conflict was described by master equations, i.e. a set of differential equations describing evolution of density $v(A,B)$ of actors of status $(A,B)$. Here we reformulate the problem in terms of probabilistic cellular automata. The obtained results for number $n(A,B)$ of actors of status $(A,B)$ are qualitatively the same as in the previous approach, both for synchronous and asynchronous version of the automaton. Namely, an enhancement of the surface status compensates a deficiency of the real one.