Updated for v0.46.

It is possible to exploit the Tiling dialog to produce a number of useful effects. The most interesting is placing tiles along an arc or spiral.

To put a tile along an arc use the P1 symmetry with one row of tiles. One use to have to resort to using a Gruppo to put tiles along a curve. As of v0.46, the Centro di rotazione is used as the center of rotation. One also used to have to specify a shift of -100%. Now one can just check the Exclude tile box.

The base tile is drawn on the left, showing the Centro di rotazione of the tile. On the right is after a P1 tiling with a per column shift removed by checking the Exclude tile box and with a rotation of 60%.

The next figure shows how 12 stars can be put in a circle. This would have been an alternative way of placing the stars in the European Union flag if the stars did not need to be placed with one of their points straight up.

Twelve stars in a circle.

This trick can also place objects along a spiral by specifying that the tile should get larger with each column. As of v0.46, one can put the stars on a logarithmic spiral so that the stars don't run into each after several loops.

Stars on a logarithmic spiral. The tile size is increased by 2.5% with Base set to 2.7. Each tile is rotated 20°.

Stars on a logarithmic spiral. The tile size is increased by 2.5% with Base set to 2.7. Each tile is rotated 20°. The per column shift has been set to 60% (with the Exclude tile box checked).

A «P1 symmetry» tiling. 8 rows, 21 columns. Rotation of -11.5° per row and 20.6° per column, Scale of 39.3% per row and 24.2% per column with a Base of 2.7 for both x and y. There pattern matches that for a pine cone with 8 rows in one direction and 13 in the other. For the mathematicians: note that 13 times the per column scaling is equal to 8 times the per row scaling and that 13 times the per column rotation minus 8 times the per row rotation is equal to 360°. This is due to the constraint that the 14th star in the first row is the same as the 9th star in the first column.

A circle tiled on an arc. The red circle with the Centro di rotazione moved off center was the source tile.