I'm Nick Rice, the creator of Begriddled puzzles.
I have self-published several books of these puzzles, available on Amazon. The first two ( Begriddled! A New Kind of Puzzle, and Begriddled! Logic) were experimental and include quite a few puzzles I spent a LOT of time creating.
Since then I have moved to creating puzzles that utilise only one of the two Begriddled rules, something I wasn't sure was generally possible when I first developed it. (It does limit what can be done, but still leaves a great deal possible.)
A puzzle consists of a grid of characters (eg numbers) and a circular sequence of ten characters, though for the logic puzzles you have to work out that sequence for yourself from "logic rules."
Begriddled rules are simple and in most of the puzzles only Rule 2 below is used.
Rule 0: Dots are dots. You simply pencil them in. (Most puzzles don't have dots so this rule doesn't apply.)
Rule 1: Except for dots, join all pairs of horizontally and vertically adjacent characters that are the same. (My newer puzzles don't have such pairs, so I omit this rule.)
Rule 2: Join all pairs of horizontally, vertically, and diagonally adjacent characters that appear next to each other in the circular sequence.
Of course with the logic puzzles you can't implement Rule 2 without having worked out what lies what to next in the sequence.