i wanted a nice border pattern to turn into a frame for a card i was making, and i came up with this fun and easy way of making it based on some g'mic filters. to remember how i made it i made an xcf of one of these patterns, where each layer represents an action, described in the layer attributes and a result, shown on the actual layer. here is the resulting border pattern of that particular xcf, but variations are endless. i'll write down the steps here, but if you prefer to look at the detailed xcf i can post that too.
1. open a new 600X600 px image
2. open g'mic and go to "patterns" ->"truchet". run filter with the following settings:
scale - somewhere between 120 and 170
radius - somewhere between 20 and 40
smoothness - 3
default settings on the rest.
3. still in g'mic, go to "contours"->"difference of gaussians" and run at default.
4. gaussian blur by 5px at this point. the resulting image will have some pixellation, gaussian blurring at this step will avoid that getting worse.
5. in g'mic, go to "deformations" -> "euclidean polar" and run at default.
6. now leave g'mic. rotate layer 90 degrees clockwise, and scale by 50%.
7. use the align tool to align it top and left. duplicate and align the copy layer right. merge down.
8. duplicate layer and flip vertically. scale layer by 50% height, but keep 100% width. merge down.
9. colourise, using whatever settings suit you, and adjust brightness and contrast if needed.