Yturralde: Impossible Figure Generator






  • This research highlights José María Yturralde’s most significant involvement and contributions to early computer art from 1968 to 1973. Yturralde collaborated with artists and scientists to expand and redefine his understanding of shapes, and explored ways that the mainframe computer could be used as a tool for complementing his art practices. He is known for developing a mathematical model with which he was able to create a highly sophisticated program where Penrose geometries could be recombined algorithmically. However, there is limited evidence and access to the code of the actual software. The authors’ goal is to further understand Yturralde’s contribution by developing a re-significance of his model, which they have accomplished through a modern interpretation of manuscripts.


  • 1. Now called Universidad Complutense de Madrid.

    2. E. Castaños Alés, Los Orígenes del arte Cibernético en España, Doctoral Dissertation (Alicante : Biblioteca Virtual Miguel de Cervantes, 2000) p. 165.

    3. E. Huhtamo and J. Parikka, eds., Media Archaeology: Approaches, Applications, and Implications (University of California, Berkeley, 2011) p. 1.

    4. Ibid., p. 3.

    5. Burbano, A. Inventions at the Borders of History: Re-Significance of Media Technologies from Latin America, Doctoral Dissertation (University of California Santa Barbara, 2013) p. 35.

    6. C. Reas, “Software Structures” (2004), retrieved 10 April 2015, <>.

    7. P. Barreiro López, La abstracción geométrica en España (1957-1969) (Madrid: CCSIC, 2009) pp. 66-67.

    8. V. Aguilera Cerni, retrieved 10 April 2015, <>.

    9. J.M. Yturralde, Interview [Sound Recording] (3 March 2014).

    10. Ibid.

    11. Castaños Alés [2], pp. 86-87.

    12. Yturralde [9].

    13. Castaños Alés [2], p. 96.

    14. Yturralde [9].

    15. Castaños Alés [2], p. 119.

    16. M. Rosen, A Little-Known Story about a Movement, a Magazine, and the Computer’s Arrival in Art, (MIT Press, 2011).

    17. Castaños Alés [2], p. 100.

    18. Ibid., p. 118.

    19. Yturralde [9].

    20. Ibid.

    21. Ibid.

    22. Castaños Ales [2], p. 132.

    23. Yturralde [9].

    24. Penrose L, Penrose R. “Impossible objects: A special type of visual illusion,” British Journal of Psychology 1958;49(1):31–33.

    25. Castaños Alés [2], p. 164.

    26. Yturralde [9].

    27. J.M. Yturralde, “Ejemplo de una aplicación metodológica continuando un trabajo sobre estructuras geométricas,” in [Art Catalog] Ordenadores en el arte (Centro de Cálculo de la Universidad de Madrid, 1969), pp. 41-45.

    28. Ibid.

    29. This is not a complete description and we are actually using directed graphs. For the interested reader a formal description of graphs as mathematical entities can be seen in any book about graph theory. A good example is: Introductory Graph Theory by Gary Chartrand. Dover Publications, 1984.

    30. Yturralde [27]. We reproduced the same geometric process described on Yturralde’s texts and sketches.

    31. One neighbor points to the Variable and the neighbor that the Variable points to.

    32. This is a very common restriction in Computational Geometry, where they like to say that the variables are in “general position.”

    33. The cases C and D look suspiciously symmetric. However, they are not the same case, since we are dealing with directed graphs.

    34. Yturralde [27].

    35. Yturralde [9].

    36. A chronology is posted on Yturralde’s website: <>. This website served as point of contact to access documentation originally published in the CCUM newsletters. The space in this article is too short to document Yturralde’s accomplishments.

    37. O. Alonso Molina. “Preciso como una gota de agua,” La Razón (18 December 1999).