Computer Art

Completion:examination (written)
Type of
Hour/semLecturesSem. ExercisesLab. exercisesComp. exercisesOther
Guarantee:Čadík Martin, doc. Ing., Ph.D., DCGM
Lecturer:Čadík Martin, doc. Ing., Ph.D., DCGM
Staudek Tomáš, Mgr., Ph.D., DCGM
Faculty:Faculty of Information Technology BUT
Department:Department of Computer Graphics and Multimedia FIT BUT
Learning objectives:
To get acquainted with the principles of mathematics and computer science in the artistic fields, to get acquainted with examples of the applied computer art, its history, current tendencies and future development, to learn practical skills from the field of computer art and realize practically artistic creations with the aid of computer.
  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).
Knowledge and skills required for the course:
  Artistic sense, basic mathematical knowledge, basic knowledge of computer graphics principles.
Learning outcomes and competences:
  Students will get acquainted with the principles of mathematics and computer science in the artistic fields, get acquainted with examples of the applied computer art, its history, current tendencies and future development, students will also learn practical skills from the field of computer art and finally, they will realize practically artistic creations with the aid of computer.
Syllabus of lectures:
  1. Towards mathematical art: Overview of art in 20th and 21st centuries.
  2. Generalized aesthetics: Visual forms of mathematical art.
  3. History of computer art: From analog oscillograms to virtual reality.
  4. Aesthetic functions I: From sinus and cosinus to the superformula.
  5. Aesthetic functions II: Generated graphics and the rhythm of algorithms.
  6. Aesthetic proportions: Golden section in mathematics, art and design.
  7. Graftals: Branching systems and models of growth in nature.
  8. Fractals I: Iterated functions systems and space-filling curves.
  9. Fractals II: From complex fractals into higher dimensions and chaos.
  10. Computational photography: introduction to computational photography, methods and principles.
  11. High Dynamic Range imaging: introduction of HDR and tone mapping techniques, possibilities and limitations.
  12. Ornaments and tiling: Symmetry, periodic tiling and interlocking ornaments.
  13. Exact aesthetics: Mathematical appraisal of shape, color and composition.
Syllabus of computer exercises:
 Practical assignments follow the lecture topics and are realized in a form of creative workshops (demonstration programs for each topic are available).
Syllabus - others, projects and individual work of students:
 Letterism and ASCII art, Digital improvisation, Generated graphics, Quantized functions, Chaotic attractors, Context-free graphics, Non-linear transformations, Quaternion fractals, Fractal landscape, Knotting, Escher's tiling, Islamic ornament, Digital collage, Graphic poster
Fundamental literature:
  • Bentley, P. J.: ;Evolutionary Design by Computers. Morgan Kaufmann, 1999.
  • Bruter, C. P.: Mathematics and Art. Springer Verlag, 2002.
  • Deussen, O., Lintermann, B.: Digital Design of Nature: Computer Generated Plants and Organics. X.media.publishing, Springer-Verlag, Berlin, 2005.
  • Grünbaum, B., Shephard, G. C.: Tilings and Patterns. W. H. Freeman, San Francisco, 1987.
  • Lord, E. A., Wilson, C. B.: The Mathematical Description of Shape and Form. John Wiley & Sons, 1984.
  • Kapraff, J.: Connections: The Geometric Bridge Between Art and Science. World Scientific Publishing Company; 2nd edition, 2002.
  • Livingstone, C.: Knot Theory. The Mathematical Association of America, Washington D.C., 1993.
  • Mandelbrot, B.: The Fractal Geometry of Nature. W. H. Freeman, New York - San Francisco, 1982.
  • Paul, Ch.: Digital Art (World of Art). Thames & Hudson, 2003.
  • Peitgen, H. O., Richter, P. H.: The Beauty of Fractals. Springer-Verlag, Berlin, 1986.
  • Pickover, C. A.: Computers, Pattern, Chaos and Beauty. St. Martin's Press, New York, 1991.
  • Stiny, G., Gips, J.: Algorithmic Aesthetics; Computer Models for Criticism and Design in the Arts. University of California Press, 1978.
  • Todd, S., Latham, W.: Evolutionary Art and Computers. Academic Press Inc., 1992.
  • Shirley, P., Marschner, S.: Fundamentals of Computer Graphics. CRC Press. 2009.
  • Szeliski, R.: Computer Vision: Algorithms and Applications, Springer. 2010.
  • Bradski, G. and Kaehler, A.: Learning OpenCV: Computer Vision with the OpenCV Library, O'Reilly. 2008.
Study literature:
  • Adams, C. C.: The Knot Book. Freeman, New York, 1994.
  • Barnsley, M.: Fractals Everywhere. Academic Press, Inc., 1988.
  • Emmer, M., ed.: Mathematics and Culture II: Visual Perfection. Mathematics and Creativity. Springer Verlag, 2005.
  • Emmer, M., ed.: The Visual Mind II. The MIT Press, 2005.
  • Glasner, A. S.: Frieze Groups. In: IEEE Computer Graphics & Applications, pp. 78-83, 1996.
  • Moon, F.: Chaotic and Fractal Dynamics. Springer-Verlag, New York, 1990.
  • Ngo, D. C. L et al. Aesthetic Measure for Assessing Graphic Screens. In: Journal of Information Science and Engineering, No. 16, 2000.
  • Peterson, I.: Fragments of Infinity: A Kaleidoscope of Math and Art. John Wiley & Sons, 2001.
  • 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.
  • Spalter, A. M.: The Computer in the Visual Arts. AddisonťWeslley Professional, 1999.
  • Turnet, J. C., van der Griend, P. (eds.): History and Science of Knots. World Scientific, London, 1995.
Controlled instruction:
  The monitored teaching activities include lectures, individual creative workshop projects, and the final exam in a form of a creative graphics application. The final exam has two possible correction terms.
Progress assessment:
  Creative workshop projects - up to 49 points (10 evaluated pieces by ~5 points):
3 points: technical realization
2 points: aesthetic quality
Final exam - up to 51 points (creative graphics application):
~15 points: concept originality
~20 points: programming intensity
~15 points: interface quality