ActionScript 3.0 :: Create Dynamic Images With 4 Lines Of Symmetry?

I can easily make a dynamic image with one or two lines of symmetry.

My normal approach is to take a square image and mirror it once too make one line of symmetry like this:

and then to make two lines of symmetry I can just mirror that image with one line of symmetry as well, making something like this:

images with 2 lines of symmetry work really well for 2D tessellations, but for 3D tessellations I need 4 lines of symmetry.

this is a problem since the way you'd normally do this is to basically fold the square in half both ways diagonally, which gives you triangles instead of rectangles.

this makes it harder to use rotation matrices to mirror the source image.

has anyone come up with a good way to give a source image that you can loop through every pixel quickly and mirror it in such a way that it has 4 lines of symmetry?

i have this completed so far, but i need the texture map to have 4 lines of symmetry, not 2 like it currently does.

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