This digital artwork features four views of the same three-dimensional object, a fractal tiling in which every tile is a similar dart shape.
The starting point is a pair of tiles matched along one long edge. A pair of smaller tiles is fit into each of the V-shaped openings in these starting tiles.
The sum of the angles at each vertex where two of the smaller tiles meet a larger tile is greater than 360 degrees, so the three tiles cannot lie in the same plane. The pairs of smaller tiles alternately buckle up and down to accommodate the fit.
This same simple rule is applied repeatedly through ten generations, resulting in the object shown. This object was created in Mathematica, and PhotoShop was used to create the montage. This is a demonstration of the way in which a complex organic structure can result from a simple set of rules being applied over and over again to a simple starting structure. The resulting object is an intriguing blend of the organic and the geometric.
Hyperbolic Fractal Tiling No. 1, by Robert Fathauer. Archival inkjet print.