He created images based on the laws of symmetry, set theory, perspective, topology and crystallography, as seen in Multiple view points and Impossible stairs: Relativity, (1953) 15, 16.Īrtists often design their work in balance and symmetry. Escher is best known to crystallographers for his successful mosaic-dividing technique. St Maurits Escher (1898–1972) is considered the father of this art direction. Van Gogh's Starry Night (1889) features chaotic vortices that accurately follow mathematical descriptions of turbulence in fluid materials, such as the turbulence of water in a river or a tornado. hypercube 14) in the two dimensional paintings in many of his works, as can be seen in The Last Supper, and The Cross. Dali depicted the four-dimensional space (e.g. Salvador Dali (1904–1989), a Spanish surrealist painter, used drawings with strong geometric-topological elements in his paintings. Examples can be seen in Illusion of the Square, and Study in Perpetual Motion 13. Leonardo da Vinci (1402–1519) used documentary geometry to create the first deformed grids, which when viewed from a certain angle appear normal. A new trend based on compression has been introduced in statistical inference, learning theory and artificial intelligence 12. Quantitative analyses of paintings from different historical periods have highlighted a number of characteristics of painting styles, such as image compression 11, entropy 1, and complexity 5. Fractal dimension represents a direct measure of the complexity of an image 9, 10.
Fractal analysis was also used to differentiate paintings of individual artists, artistic directions and historical periods.
These analyses have shown that Pollock is a unique artist of gestural expressionism due to his painting of complicated line patterns, which consistently comply with fractal scaling criteria.
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The analysis of the complexity of Jackson Pollock’s artwork was approached by fractal analysis 6, indicating a series of similarities between Pollock's artistic expression and fractals 7. The characteristics of an artwork can be quantified and compared by considering characteristics such as shape, colors and brightness 4, 5. An objective quantification of an artwork presents a challenge, and as such new objective methodological approaches become a necessity 1, 2, 3.
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