Patterns are the Asperger's child's dream come true. We see patterns everywhere, even when others don't notice them. Aspie behaviour is, to some extent, governed by patterns.
Parents of aspies often think that their children don't show Asperger's tendencies towards patterns. Sometimes, you just need to know where to look...
Example 1. My 7 year-old son seems to wander all over the place when we're walking in the shops. My non-aspie (NT) wife just thought he was mucking around but when I went with him, I immediately became aware that he was walking in patterns on the tiles. Since the coloured pattern zig-zagged across the shopping center and he was following it, he seemed to be all over the place.
It should be noted that this is very similar to the notion that Asperger's children cannot "step on a crack". Of course, that reasoning is quite flawed and asperger's people can quite comfortably step on cracks depending upon the pattern that they're following at the time. Indeed, occasionally the pattern will be step ONLY on cracks. I don't know where the rules for which pattern is in effect at any given time come from, they just "exist".
Example 2. My 4 year-old son was playing with some puzzle pieces. At one point he stopped putting them in the puzzle and started collecting them together in groups. It quickly became obvious that he was building a pile of red pieces, one of yellow, one of blue etc..
Another thing that my 4 year-old does is line his matchbox cars up in neat little rows. I remember doing that when I was a kid. Somehow, it just seemed to be the natural order.
Adult aspie behaviour includes things like, Matching the colour pegs when hanging out the washing (ie: two pegs of the same colour per item). I used to go to the extreme of hanging my wife's clothes out on one quarter of the line with red pegs, mine with blue, household items (blankets etc) with yellow, and so on. There's too many clothes and not enough pegs for me to do that now but I still tend to match my peg colours on the same garment.
Can an aspie cope with something that is out of pattern or not lined up?
In general, yes. Obviously they prefer things to be lined up, properly sequenced and in pattern. Lack of order does irritate the aspie but at least by adulthood, they've learned that perfection is an unattainable ideal.
When I was younger, I'd be forever fixing my bookcase so that the books stayed lined up neatly, not pushed in. As an adult however, I'm not so worried about that. I do however get annoyed when books in a series have covers that just don't line up properly or when a publisher changes styles halfway through. (Stephen King's Dark Tower Sequence is a good example of this).
What can parents do?
Other than help your child get over the fact that things won't be perfect no matter how hard they try, there's nothing else you need to do.
Use Patterns for Learning!
Patterns are the basic building blocks of the universe. Patterns can be found almost anywhere and since aspies are excited by them, they can be used to help them to learn.
At school, my mathematics would always improve whenever I could see a pattern in the type of equations we were studying. The same goes for English and spelling, where similar sounding words have patterns in them.
The one thing that I had lots of problems with at school was Chemistry. I noticed years later than I'd even written in my exercise book that the subject "sucked" because they kept changing the rules and there was not obvious pattern. If something doesn't seem to have an obvious pattern (the periodic table for one), you should work towards helping your children to find one. Even if you have to add something unrelated yourself.