Tileable textures that stay seamless when rotated?
So, I am working on a dungeon tile project, and I've hit a snag. While there are a lot of amazing texture programs (I use Genetica) that create amazing and seamless textures, they are only entirely seamless when the textures are "slid" and not rotated. So, let's use cardinal directions for the metaphor: the "north" side tiles perfectly when touching the "south" side of the same texture, and same goes for the "east" with the "west" but I want to create a truly seamless texture so that aligning, say, 'north' with 'west' or even 'north' with 'north' will still look natural with no interruptions in the texture.
I can probably blunder through it myself, but if anyone knows of any tutorials, techniques, or software that automates this, I would love to hear about it!