Septets of Three Flowers by Tis Veugen

About "Septets of Three Flowers"

by Tis Veugen

About the artwork

This non-periodic image with 7-fold rotation symmetry around the sunflower is made of deformed rhombi of 3 categories. In each of the 7 directions the rhombi have a (slightly) different deformation, so that there are 7*6/2 = 21 prototiles, each with a different shape. Similar prototiles have only translation symmetry. There are 7 rhombi (called S) with angles of Pi/7 and 6*Pi/7, 7 rhombi (called D) with angles of 2*Pi/7 and 5*Pi/7, and 7 rhombi (called W) with angles of 3*Pi/7 and 4*Pi/7. The S-prototiles form a sunflower which requires 7 pairs of tiles since 14 * Pi/7 = 2*Pi. The opposite acute angles of these tiles meet in the center of the sunflower. The sunflower picture has no rotation or mirror symmetry; it is cut into 14 pieces, and 2 opposite pieces are rendered in a single prototile requiring some image editing. The 7 D-prototiles form a dahlia with a (original) pink heart. By moving each prototile to the other side of the center, you get the same dahlia, but colored a little blue. This artificial blue coloring is done to show that the dahlia with the blue heart is built differently. The W-prototiles come from a water lily. Since 3 does not divide 14, these tiles cannot reconstruct a complete water lily, at least not in this composite image. In fact the W-prototiles can reproduce the water lily, but then they would overlap. In any case, neighboring prototiles of a same category can be considered as continuous images.
The multigrid approach of N.G. de Bruijn, my former professor, has been applied to construct the whole image. The sunflower is the origin of the construction. Based on the scale factor used, the next complete sunflower would be about 48000 pixels away. This picture has 9000 x 9000 pixels.