If you're used to the square grid from standard Slitherlink, variant puzzles initially look pretty daunting. But however disorienting the grids may initially seem, many patterns you know from standard Slitherlink apply to arbitrary grids.

To start with, here are some very basic arbitrary patterns (created by taking a screenshot from a puzzle here):

1) A big number in a corner or at the edge of a puzzle always allows you to draw some lines:




2) Two adjacent very big numbers (= 1 less than the respective number of their surrounding edges). Example: The familiar pattern of two adjacent 3s in a square grid.




In this case, depending on the grid, the details of the pattern will differ, but there will always be a similar pattern.

Many patterns are analogous to those posted in this old thread. Probably need someone to generalize all rules

Most of the patterns in Standard Slither Link transfer well to the Variations patterns, but I liked how the grid in this pattern of 1s allows you to deduce three crosses and three lines, whereas in a square grid, you can't deduce a single line or cross in an arbitrary pattern of 1s.

I never quite understood Jankonyex's intuition for how the pattern they posted above worked, but now here ("Tracing numbers across edges (Friday, 12th November 2021)") is a thread explaining that specific pattern in a hexagonal grid, and maybe it applies to arbitrary grids?

Yeah, I think that is what he's showing. In his pattern two numbers either connect diagonally at a 4-way intersection (similar to the square grid, 1 line on one side means 1 line on the other) or adjacently with a >-< shaped pattern (2 lines on one side means 2 lines on the other).