oh, another thing you can try.
again, let's assume that your texture is to be 1024x1024
Make a new image at 2048x6144 (huge, i know). Fill your pattern. Scale it to 2048x2048 using Bicubic Sharper (if you use 1 pixel wide lines, you might run into problems with Bicubic Sharper). Run a gaussian blur at 0.1 or 0.2, run Polar Coordinates, run the gaussian blur again, and take the inner 1024x1024.