# Emergence of fractal in aggregation with stochastic self-replication

Source: [Emergence of fractal in aggregation with stochastic self-replication](<https://www.sota2.com/research/paper/68fa2cb71e209131ce852b7a>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-24T15:32:04.188Z

Authors: M. K. Hassan, M. Z. Hassan, N. Islam

Published: 2013-07-30T03:58:44.000Z

## Abstract

We propose and investigate a simple model which describes the kinetics of aggregation of Brownian particles with stochastic self-replication. An exact solution and the scaling theory are presented alongside numerical simulation which fully support all theoretical findings. In particular, we show analytically that the particle size distribution function exhibits dynamic scaling and we verified it numerically using the idea of data-collapse. Besides, the conditions under which the resulting system emerges as a fractal are found, the fractal dimension of the system is given and the relationship between this fractal dimension and a conserved quantity is pointed out.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1307.7804>)

[PDF](<https://arxiv.org/pdf/1307.7804.pdf>)