Untitled Impossible Figure (red cube)

In 1968, at the University of Madrid’s Calculus Centre, José María Yturralde began programming geometric forms that turned mathematical logic into visual structure. The Centre, newly established with the university’s first computer, fostered collaboration among artists, architects, and scientists exploring the creative potential of technology. A year later, Yturralde held his first solo exhibition, “Formas Computables” (Computable Forms), recognized as the first presentation of computer-generated art in Spain.

The works from this period mark the beginning of Yturralde’s lifelong exploration of mathematics, perception, and form. From 1968 to 1973, he built on the research initiated at the Calculus Centre to develop his Impossible Figures series, in which geometric precision became a tool for creating visual paradoxes. Influenced by Roger and Lionel Penrose’s studies of “impossible objects,” he examined how mathematical logic could give rise to forms that seem possible yet defy physical space.

A work from 1971 distills the idea of the Impossible Figures series to its most essential form. A single angular structure floats against a dark ground, its planes rendered in gradients of red and yellow that suggest light and volume while never settling into fixed perspective. We follow its edges as they fold and twist, forming a shape that is both concrete and elusive. Another member of the series from 1972 expands this exploration into a grid of interlocking red cubes. Subtle variations in tone and alignment cause the structure to shift between depth and flatness. As we observe, order becomes unstable and geometry begins to reveal its own uncertainty.

This series laid the groundwork for Yturralde’s later explorations of spatial perception and light in three-dimensional space, including the Flying Structures he developed during his time at MIT.