ABSTRACT
This chapter focuses on one particular use of 'fractal' and the application to painting of the theory associated with it. Fractals are geometrical figures, just like circles, triangles or rectangles, but have special properties that distinguish them from other geometrical figures: self-similarity, fractional dimension, formation by iteration. The difference between fractals and other geometrical figures has been described in somewhat different ways. Fractals are shapes that show similar features at different sizes. The Pythagoreans argued for an objectivistic account of beauty, because, in the words of Tatarkiewicz, 'beauty is constituted by harmony, harmony derives from order, order from proportion, proportion from measure and measure from number'. According to the classic account of beauty in terms of organic unity, heavily influenced by the Pythagoreans, beauty is thus objective in a stronger sense than the phenomenological one. A small change of the internal organisation of the work may ruin its beauty.
