Fractal Sudoku Object: Gallery

Fractal Sudoku Object

Fractal Sudoku Object

This is a second-iteration approximation of a stacked hexagonal pyramid fractal, composed of 81 such pyramids. It is enclosed in a transparent acrylic 32-faced polyhedron. This polyhedron has 12 square faces, 6 of which are outlined in red and the other 6 in yellow.

When the object is viewed directly through any of the 12 square faces, the gaps between components align perfectly, giving the appearance of a flat square shape—whether through the red frames or the yellow ones.

In these square views, the 81 stacked hexagonal pyramid pieces appear as 81 squares arranged in a 9×9 grid. These 81 pieces are colored in 9 different colors, and from each of the 12 square views, each row, each column, and each 3×3 block contains all 9 colors exactly once. In other words, from any of the 12 square directions, the coloring satisfies the conditions of a Sudoku solution. There are 30 such colorings (excluding symmetries) that satisfy this condition for this second-order fractal. The coloring used in this object is the one with the highest degree of symmetry among them.

When viewed from other directions, the object reveals a wide variety of additional geometric forms.

This work was exhibited and presented at the Bridges Conference on Mathematics and the Arts, held in San Sebastián, Spain from July 24–27, 2007. For this exhibition, an acrylic-framed version of the object was created, featuring square faces made from pink and yellow acrylic.