VIN Acad. year 2021/2022 Winter semester 5 credits
In this course we explore the places where art, mathematics and algorithms meet. The course consists of introduction into computer art, computer-aided creativity in the context of generalized aesthetics, a brief history of the computer art, aesthetically productive functions (periodic functions, cyclic functions, spiral curves, superformula), creative algorithms with random parameters (generators of pseudo-random numbers with different distributions, generator combinations), context-free graphics and creative automata, geometric substitutions (iterated transformations, graftals), aesthetically productive proportions (golden section in mathematics and arts), fractal graphics (dynamics of a complex plane, 3D projections of quaternions, Lindenmayer rewriting grammars, space-filling curves, iterated affine transformation systems, terrain modeling etc.), chaotic attractors (differential equations), mathematical knots (topology, graphs, spatial transformations), periodic tiling (symmetry groups, friezes, rosettes, interlocking ornaments), non-periodic tiling (hierarchical, spiral, aperiodic mosaics), exact aesthetics (beauty in numbers, mathematical appraisal of proportions, composition and aesthetic information). The course is lectured by Tomáš Staudek.
Language of instruction
Course Web Pages
Subject specific learning outcomes and competences
- Students will acquire both theoretical and applied competence in software aesthetics.
- Students will be able to interpret and evaluate algorithmic works of art.
- Students will deepen creative skills by fulfilling practical graphic assignments.
The aim of the course (http://artgorithms.droppages.com) is to get acquainted with the principles of mathematics and computer science in the artistic fields, to understand theoretical foundations of algorithmic creativity and software aesthetics, to get an overview of applied computer art, to apply practical skills from the field of software aesthetics, realizeand criticize artistic creations with the aid of computer.
Why is the course taught
In this course we look at algorithms from the artistic perspective. Many practical calculations offer aesthetic qualities which can be acheived with common mathematical knowledge supported with appropriate tools. The course introduces principles of computer-aided art (aesthetic functions, transformations, proportions, visual grammars, fractals, artistic tessellation). Lectures are divided into theoretical part covering computational foundations of art, and practical assignmnets supported with computer graphics applications. The course objective is to develop students' independent creative skills.
Prerequisite kwnowledge and skills
The course assumes creative mind, artistic thinking, basic mathematical knowledge, basic knowledge of computer graphics principles.
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- Bentley, P. J.: Evolutionary Design by Computers.Morgan Kaufmann, 1999.
- Deussen, O., Lintermann, B.: Digital Design of Nature: Computer Generated Plants and Organics.X.media.publishing, Springer-Verlag, Berlin, 2005.
- Glasner, A. S.: Frieze Groups. In: IEEE Computer Graphics & Applications, pp. 78-83, 1996.
- Grünbaum, B., Shephard, G. C.: Tilings and Patterns. W. H. Freeman, San Francisco, 1987.
- Livingstone, C.: Knot Theory. The Mathematical Association of America, Washington D.C., 1993.
- Lord, E. A., Wilson, C. B.: The Mathematical Description of Shape and Form. John Wiley & Sons, 1984.
- Mandelbrot, B.: The Fractal Geometry of Nature. W. H. Freeman, New York - San Francisco, 1982.
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- Ngo, D. C. L et al. Aesthetic Measure for Assessing Graphic Screens. In: Journal of Information Science and Engineering, No. 16, 2000.
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- Pickover, C. A.: Computers, Pattern, Chaos and Beauty. St. Martin's Press, New York, 1991.
- Prusinkiewicz, P., Lindenmayer, A.: The Algorithmic Beauty of Plants. Springer-Verlag, New York, 1990.
- Schattschneider, D.: Visions of Symmetry (Notebooks, Periodic Drawings, and Related Work of M. C. Escher). W. H. Freeman & Co., New York, 1990.
- Sequin, C. H.: Procedural Generation of Geometric Objects. University of California Press, Berkeley, CA, 1999.
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- Stiny, G., Gips, J.: Algorithmic Aesthetics; Computer Models for Criticism and Design in the Arts. University of California Press, 1978.
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- Turnet, J. C., van der Griend, P. (eds.): History and Science of Knots. World Scientific, London, 1995.
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- Caplan, C. S. The Bridges Archive. The Bridges Organization, 2013.
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- Emmer, M., ed.: The Visual Mind II. The MIT Press, 2005.
- Friedman, N., Akleman, E.: HYPERSEEING. The International Society of the Arts, Mathematics, and Architecture (ISAMA), 2012.
- Kapraff, J.: Connections: The Geometric Bridge Between Art and Science. World Scientific Publishing Company; 2nd edition, 2002.
- Manovich, L.: Software Takes Command. Bloomsbury Academic, 2013.
- McCormack, J., et al.: Ten Questions Concerning Generative Computer Art. Leonardo: Journal of Arts, Sciences and Technology, 2012.
- Peterson, I.: Fragments of Infinity: A Kaleidoscope of Math and Art. John Wiley & Sons, 2001.
- Radovic, L.: VisMath. Mathematical Institute SASA, Belgrade, 2014.
Syllabus of lectures
- Towards mathematical art: art in the 20th and 21st centuries.
- Software aesthetics: visual forms of computer art.
- History of computer art: from the oscilloscope to interactive media.
- Aesthetic functions: from sinus and cosinus to the superformula.
- Aesthetic transformations: repetition, parametrization and rhythm of algorithms.
- Aesthetic proportions: golden section in mathematics, art and design.
- Spirals and graftals: models of growth and branching in nature.
- Geometric fractals: iterated functions and space-filling curves.
- Algebraic fractals: from the complex plane to higher dimensions.
- Chaotic fractals: visual chaos of strange attractors.
- Symmetry and ornament: periodic tiling and interlocking mosaics.
- Nonperiodic and special ornament: spiral, hyperbolic and aperiodic mosaics.
- Mathematical knots: knots and braids from the Celts to modern topology.
Syllabus of computer exercises
Syllabus - others, projects and individual work of students
Creative assignments follow the lecture topics and are realized in a form of non-supervised projects supported by freely available creative applications for each topic. Outputs will be exhibited in the students' gallery.
- Letterism and ASCII art
- Digital improvisation
- Computer-aided rollage
- Generated graphics
- Quantized functions
- Algorithmic op-art
- Evolutionary algorithms
- Chaotic attractors
- Context-free graphics
- Fractal flames
- Quaternion fractals
- Fractal landscape
- Escher's tiling
- Islamic ornament
- Circle limit mosaics
- Digital collage
- Graphic poster
- Artistic image stylization
- Generated sculpture
Creative assignments -- up to 50 points (at least 10 evaluated pieces by 5 points):
- 3 points: technical realization and aesthetic quality
- 1 point: exhibition in the course gallery
- 1 point: timely submission
Final project -- up to 50 points (creative graphics application):
- 15 points: concept originality
- 20 points: programming intensity
- 15 points: interface quality
The monitored teaching activities include lectures, creative assignments, and the final project in a form of a creative graphics application. Classes are supported by elearning activities in LMS Schoology. Students are responsible for reading and watching provided materials and participating in class discussions.
Assignments are provided in the form of individually elaborated projects. The classified credit has two possible correction terms.
The final grade corresponds to the points earned during the semester. Students will pass the course after accomplishing half of assignments (50 points). Final project (another 50 points) consists from creating an application for artistic creativity and presenting its creative potential. The application shall be executable on an appropriate platform (Win, OSX, iOS, Linux, Android). Extra points can be attributed for class activity.
Course inclusion in study plans
- Programme IT-MSC-2, field MBI, MBS, MIS, MMM, MPV, MSK, any year of study, Elective
- Programme IT-MSC-2, field MGM, 1st year of study, Elective
- Programme MITAI, specialisation NADE, NBIO, NCPS, NEMB, NGRI, NHPC, NIDE, NISD, NISY, NMAL, NMAT, NNET, NSEC, NSEN, NSPE, NVER, NVIZ, any year of study, Elective