Programme Catalogue & ECTS Guide

Fractal Methods in Computer Graphics Field of study: Computer Science
Programme code: W4-S2IN19.2022

Module name:	Fractal Methods in Computer Graphics
Module code:	W4-IN-S2-20-F-MFwGK
Programme code:	W4-S2IN19.2022
Semester:	summer semester 2025/2026 winter semester 2025/2026 summer semester 2024/2025 winter semester 2024/2025 summer semester 2023/2024 winter semester 2023/2024
Language of instruction:	Polish
Form of verification:	course work
ECTS credits:	4
Description:	Aim of the classes is to introduce to the students the basics of fractal theory and its applications in computer graphics. Various types of fractals and effective methods of their rendering will be presented. Moreover, the applications of fractal theory in image processing and compression, and in the aesthetics evaluation will be presented. During the course, the students will prepare projects in teams of maximum two and present results of their work in the form of presentation in front of the group.
Prerequisites:	(no information given)
Key reading:	* Barnsley, M.F.: Fractals Everywhere, 2nd Edition. Morgan Kaufmann, San Francisco (1993) * Barnsley, M.F.: Superfractals. Cambridge University Press, Cambridge (2006) * Kalantari, B.: Polynomial Root-finding and Polynomiography. World Scientific, Singapore (2009) * Kotarski, W.: Fraktalne modelowanie kształtu. EXIT, Warszawa (2008) * Martyn, T.: Algorytmy geometryczne w wizualizacji fraktali układów odwzorowań iterowanych. Oficyna Wydawnicza Politechniki Warszawskiej, Warszawa (2011) * Shier, J.: Fractalize That! A Visual Essay on Statistical Geometry. World Scientific, Singapore (2019) * Sprott, J.C.: Elegant Fractals - Automated Generation of Computer Art. World Scientific, Singapore (2019) * Various research papers on fractals

Learning outcome of the module	Codes of the learning outcomes of the programme to which the learning outcome of the module is related [level of competence: scale 1-5]
Knows and understands various types of fractals used in computer graphics, in particular: complex fractals, inversion fractals, iterated function system fractals, L-systems, strange attractors. [M_001]	K_W01 [1/5] K_W02 [1/5]
Knows and understands the basic algorithms used in fractal theory, in particular: chaos game, complex fractals rendering algorithms, fractal dimension computation. [M_002]	K_W04 [1/5]
Knows and understands mathematical notions used fractal theory, in particular: contractive mapping, metric, mappings composition, iterative process, dynamical system. [M_003]	K_W01 [1/5]
Can obtain information about fractals and computer graphics from literature, databases and other sources. [M_004]	K_U01 [1/5] K_U07 [1/5]
Can work individually and in a team. [M_005]	K_U02 [1/5]
Can prepare and present a presentation on execution of project's task. [M_006]	K_U03 [1/5] K_U04 [1/5]
Can think and act creatively. [M_007]	K_K01 [1/5] K_K03 [1/5]

Type	Description	Codes of the learning outcomes of the module to which assessment is related
Project [W_001]	Preparing the project and presentation of the chosen topic connected with fractals.	M_001 $<div style="white-space:pre-wrap">Knows and understands various types of fractals used in computer graphics, in particular: complex fractals, inversion fractals, iterated function system fractals, L-systems, strange attractors.</div>$ M_002 $<div style="white-space:pre-wrap">Knows and understands the basic algorithms used in fractal theory, in particular: chaos game, complex fractals rendering algorithms, fractal dimension computation.</div>$ M_003 $<div style="white-space:pre-wrap">Knows and understands mathematical notions used fractal theory, in particular: contractive mapping, metric, mappings composition, iterative process, dynamical system.</div>$ M_004 $<div style="white-space:pre-wrap">Can obtain information about fractals and computer graphics from literature, databases and other sources.</div>$ M_005 M_006 M_007
Reports [W_002]	Solving sets of tasks.	M_001 $<div style="white-space:pre-wrap">Knows and understands various types of fractals used in computer graphics, in particular: complex fractals, inversion fractals, iterated function system fractals, L-systems, strange attractors.</div>$ M_002 $<div style="white-space:pre-wrap">Knows and understands the basic algorithms used in fractal theory, in particular: chaos game, complex fractals rendering algorithms, fractal dimension computation.</div>$ M_003 $<div style="white-space:pre-wrap">Knows and understands mathematical notions used fractal theory, in particular: contractive mapping, metric, mappings composition, iterative process, dynamical system.</div>$ M_005

Form of teaching			Student's own work		Assessment of the learning outcomes
Type	Description (including teaching methods)	Number of hours	Description	Number of hours	Assessment of the learning outcomes
lecture [Z_001]	Presenting educational content using audiovisual methods.	15	Independent study of lecture topics and given literature.	15	Project [W_001] $<div style="white-space:pre-wrap">Preparing the project and presentation of the chosen topic connected with fractals.</div>$
laboratory classes [Z_002]	Detailed preparation of the students to: (1) the use of various fractal method in computer graphics, (2) the development of new methods. Solving programming tasks.	30	Familiarizing with subject of the laboratory. Familiarizing with subject of the project and preparing it in a team. Preparing a presentation of the project.	60	Project [W_001] $<div style="white-space:pre-wrap">Preparing the project and presentation of the chosen topic connected with fractals.</div>$ Reports [W_002]

Attachments
Module description (PDF)

Information concerning module syllabuses might be changed during studies.

Syllabuses (USOSweb)
Semester	Module	Language of instruction
(no information given)

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