Fagella Rabionet, NúriaTorralba Agell, Adrià2021-07-062021-07-062020-06-21https://hdl.handle.net/2445/178855Treballs Finals de Grau d'Enginyeria Informàtica, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2020, Director: Núria Fagella Rabionet Anna Puig Puig[en] When a holomorphic function is iterated, it generates a dynamical system on the complex plane. In this project we describe both the local and global theory of the different orbits of holomorphic functions, focusing on the polynomial families. We present the necessary results leading to two algorithms to draw both Julia sets and Mandelbrot (and Multibrot) set: the Escape Algorithm and Henriksen Algortihm. In addition, we present the development of an interactive application, made with Unity, that allows us to visualise fractals on the complex plane -rendered using the aforementioned algorithms- and a generalisation of them over a 3-dimensional space, directly on a website.123 p.application/pdfengmemòria: cc-nc-nd (c) Adrià Torralba Agell, 2020codi: GPL (c) Adrià Torralba Agell, 2020http://creativecommons.org/licenses/by-nc-nd/3.0/es/http://www.gnu.org/licenses/gpl-3.0.ca.htmlFractalsSistemes dinàmics complexosProgramariTreballs de fi de grauFuncions holomorfesComplex dynamical systemsHolomorphic functionsComputer softwareBachelor's thesesinfo:eu-repo/semantics/bachelorThesisinfo:eu-repo/semantics/openAccess