How do I make a seamless hex tile that can be rotated?

In this post, I describe one way of making a hex tile that can be tiled seamlessly, even when the tiles are rotated by (different) multiples of 60 degrees. This is a quick-and-dirty method, and works well only for certain types of tiles.

1Make a seamless hex tile as explained in How do I make a seamless hex-tile? But do not perform the final crop. If you used the second method, you will have a diamond-shaped image, like this:

2Duplicate the layer until you have six. Rotate the layers as follows:

6 (Top)	300
5	240
4	180
3	120
2	60
1 (Bottom)	0

(I usually duplicate the top layer, turn it by 60 degrees, and repeat until I have 6 layers).

3Set the layer opacities as follows:

6 (Top)	16.6%
5	20%
4	25%
3	33.3%
2	50%
1 (Bottom)	100%

This will make all 6 layers equally visible.

4Flatten the layers.

5Crop the hexagon from the center of the image. If you used Method 2 for creating the seamless hex tile, your hex will have half the height of the diamond you started with.

Enhancements

Other transparency modes

You can use other transparency modes, but you have to make sure that each layer has equal weight in the final composite. For example, if you use addition, you need not set the opacities. (You would probably make the layers much darker, to prevent oversaturation). Here is an informal guide to blending layers for this purpose:

Normal, Dissolve: Opacities from bottom to top: 100%, 50%, 33.3%, 25%, 20%, 16.6%.
Addition, Lighten, Screen: All opacities 100%; make images darker.
Multiplication, Darken: All opacities100%; make images lighter.
Difference, Exclusion: All opacities 100%. (The result does not resemble the original at all).