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Now that I've written all that, I'm actually not even sure what the OP means when talking about "patterns." That word is not so restrictive as you seem to think it is.
The very first "Complete the pattern" puzzles are all about seeing the bigger picture and just finish the picture that it looks like a continous pattern.
In future puzzles your brain will automatically lock in into searching for visual patterns that repeat to continue the pattern of the picture, not expecting to be a pattern like "4 black - 5 white equals white"
Take for example the number series
1,2,4,8,16,32
It's a number pattern with a rule that dictates the next number.
The game does lull players into a false assumptions by having the first few puzzles be simply mirroring the color shapes.