Abstract

This callistical thesis is a radical investigation of the relationship between the algorithmic beauty of computer generated fractals, the algorithmic beauty of nature, and the fractal beauty of the world's best known artistic masterpieces, from classical visual objects dependent on the golden section proportion to the fractal nature of the best known 20th century painters. The essence of the fractal is a dynamic symmetry of self-generated self-similar proportional relationships and ordered scaling---every element of the fractal resembles every other part. The essence of the golden section is also a self-generated dynamic symmetry of self-similar proportional relationships across scale. All of organic nature is fractal and there is a natural reason why humans universally delight in the fractal beauty of a tree and not in a telephone pole. But besides examining the fractal/organic nature of beautiful objects, natural or artificial, the thesis also examines the latest, but unproven scientific hypotheses as to the fractal nature of brains and minds, and the possibility that human experience is somehow based on an unconscious dynamic algorithmic interaction between world, brain and mind. The thesis offers the radical hypothesis that the closest humans may ever come to consciously experiencing this interconnection between world, brain, mind is the unique beauty experience. ;The revolutionary discovery that there is a geometric determinism underlying nature's continual flux has its roots in the tradition of natural philosophy that goes all the way back to Pythagoras, Hereclitus, Anaxagoras and Plato, and their use of geometric models to illustrate the complex nature of the universe . Therefore, this thesis examines the pre-Socratic philosophical and artistic understanding of beauty as symmetry, eurhythmy, and unity in diversity. Using the long forgotten way of dividing a line into incommensurate magnitudes in order to form a dynamic symmetry of commensurate plane areas, the thesis clearly demonstrates that Plato's divided line, like Pythagoras' pentagram, are the same golden section proportion that artists have been using throughout history to create their beautiful temples, sculptures and art objects. The thesis in using one of the most revolutionary discoveries of modern science, ends up being a re-validation of some of the oldest philosophical and artistic intuitions---most specifically that underlying nature's continual change there is a complex unchanging order---a geometric stability which cannot be divorced from the concept of beauty. God is a geometer