I just look for patterns. Sometimes it's glances my eyes across it all, finding things that visually look similar and working out how they're inter-connected. Sometimes it's a form of cross-referencing trial and error, where I test a theory out (ie. what if the pattern is X? Does that work consistently?). I also do a horizontal/vertical/diagonal/clockwise/anti-clockwise etc scan to see if things flow in an obvious directional pattern.
I would say these sorts of tests are very Ne friendly, and in that sense are biased. A lot of it is about how quickly your brain can unscramble seemingly random nonsense into a clear structure. Good usage of Te probably helps too because it sets good groundwork for common lines of logical thought. I don't doubt other methods (and functions) can work very effectively but perhaps it comes less naturally and is therefore more time consuming and mentally straining.
Can I ask why it bothered you that the logic was vertical/horizontal rather than Sudoku-style?