K. Wroblewski
Friday 9 November 2018 by Libadmin2018


The game of space was and still is a crucial aspect of visual arts. The aim of this study is to examine how the arrangement of hues, rhythms and angles of various polygons can create an impression of depth and movement on a flat surface. The so-called Penrose tiling and Ulam’s spiral are mathematical models that have been applied for the painting experiment. There is a vast amount of evidence gathered over the ages that shows art is strictly interrelated with science. It refers both to music, literature, architecture and the visual arts as well. Since the Renaissance, painters and architects have employed descriptive geometry, mathematics and linear perspective in order to operate with correct proportions but also to create both the illusion and distortion of space. At the beginning of the twentieth century, painters released themselves from realism and gained a new approach towards the picture. Discoveries from natural science allowed them to perceive the phenomenon of light and colour as a vibration of wavelengths. When Euclidean geometry was abandoned, the non-Euclidean space-time universe and the quantum realm came on stage together with the various types of abstract art, which are still present in our postmodern era. In the mid-seventies of the last century, English mathematician and physicist Roger Penrose published a non-periodic sets of patterns. These constructions have been based on five-fold symmetry. During my painting experiment the polygons shaped by Penrose were deconstructed through additional axes of symmetry. On to the new structure I applied sequences of primary and secondary colours. This operation revealed an unexpected rhythm of shapes and colour configurations. Although a new space was opened, the original symmetry remained. A similar study was carried out with use of Ulam’s spiral, which is a graphical layout of prime numbers. In this case, the primes appear on a quadratic lattice in diagonal, vertical and horizontal rows, creating unique patterns, irregular intervals and gaps. The main finding of this artistic and theoretical study is the statement that each irregularity has its own logic and order. The non-periodical nets of shapes and colour shades reflect the complex structure of the entire universe.

Keywords: art and science, contemporary art, painting, geometry, rhythm, colour

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