Settings: Formula 51, Render 4 Orbit Counting, Inside-Out, Color 14-1 modified, Transform 3 arctan.
I played with every color mixing parameter (except Saturation and Offset which I leave alone) to arrive at this. Most importantly I lowered the Render setting from 1.000 to 0.260. Lowering the Render setting can sometimes give amazing results. This image is tileable because each side of the fractal is a mirror image and I aimed my "camera" directly at the midpoint.