Construction of Fractal Sets by Iterated Function Systems

• Grant number: 24/01726-0
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: May 01, 2024
• End date: December 31, 2025
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Tiago Pereira da Silva
• Grantee: Ana Cláudia Rodrigues e Silva
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Associated research grant: 13/07375-0 - CeMEAI - Center for Mathematical Sciences Applied to Industry, AP.CEPID

Abstract

The study of random dynamical systems is extremely relevant for the modeling and understanding of various natural systems (such as climatic dynamics and certain classes of dynamic programming problems, for example). The present project aims to investigate and construct fractal sets from the perspective of iterated function systems. Starting with the construction and study of the Barnsley-Hutchinson operator, progressing to the development of the Barnsley chaos game, we will construct important fractal sets