| Several scholars have noted that the two greatest revolutions in art, the Renaissance and the birth of Modern Art, were catalyzed by artists thinking about new geometries: perspective geometry for the former, non-Euclidean and higher-dimensional geometry for the latter. |
| Samuel Edgerton makes a long, entertaining, and convincing argument about the years 1300, 1400, 1500, and painters' open adoption of Euclid after it was brought (in Arabic) from Spain to Tuscany. Some Renaissance artists - Filippo Brunelleschi and Leon Baptista Alberti, for example - wrote about perspective geometry, but the lead came from geometry. |
| Linda Dalrymple Henderson thoroughly explores the influence of non-Euclidean and higher-dimensional geometries on the birth of modern art. Indeed, Henderson states that these geometries, and not relativity, were the main scientific influence on modern art. Dali's The Crucifixion (Corpus Hypercubicus) (1954) uses an unfolded hypercube for the cross. For another example of Dali's explicit interest in four-dimensional geometry, see the photograph on page 110 of Banchoff. |
| Rhonda Roland Shearer speculates that fractal geometry may bring about a new revolution in art. Some of her own work, combining Euclidean geometric objects with the natural fractal forms of plants, points to some of the new vistas fractal geometry may open. Indeed, Shearer notes the eight traits of a scientific revolution and illustrates those traits obviously exhibited by fractal geometry. For example, fractal geometry is a new language for the irregularity of nature, gives a new perspective on part/whole relationships (through self-similarity), and is a powerful new cultural icon. |
| We will welcome this fractal revolution in art if it happens. We note some artists, including Dali, already have seeded the beginnings of this revolution. |