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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/178855
Iteration of holomorphic functions and visualisation of fractals
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[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.
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Treballs Finals de Grau d'Enginyeria Informàtica, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2020, Director: Núria Fagella Rabionet Anna Puig Puig
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TORRALBA AGELL, Adrià. Iteration of holomorphic functions and visualisation of fractals. [consulted: 7 of October of 2026]. Available at: https://hdl.handle.net/2445/178855