Godel, Escher, Bach: Just Another Braid
This paper describes the synthesis of two completely different minimal art techniques applied in a new type of mathematical art. The portraits of Godel, Escher and Bach are chosen to demonstrate this. The combined techniques are minimal art objects and optical minimal art graphics. Minimal Art Objects Our earlier contributions in creating minimal art objects are described in [1] and [3] An example is shown in Figure 1. Figure 1: Minimal Art Object. Such a minimal art object consists of n x n elements (cubelets) filling a n x n x n space in such a way that it has 3 projections of n x n squares. These 3 projections are perpendicular to each other. The design rules to create such an object obey the rules of the Latin square. A Latin square is a n x n array filled with n different numbers, each occurring exactly once in each row and exactly once in each column. In our object each number is represented by a cubelet, which position in space is determined by its position in the Latin square (in x and y) and the number itself representing the height level (z) The cubelets are connected on the edges into one object. This connectivity of the cubelets asks for further constraints of the Latin square. For this project we use an object with 256 connected cubelets in a 16 x 16 x 16 space, based on the 16 x 16 Latin square of Figure 2. Bridges Finland Conference Proceedings