Up in Devonport, he spent a lot of his time sitting on a soccer ball, drawing and calculating on a pad. He spent most of day 1 drawing an intricate map of a made-up continent. Judging by the arrows one country was invading another one. I used to do the very same thing - I have NOT taught him how to do this but he does read a lot of the same books I did as a kid - 1950s and 60s geography textbooks that my dad once taught from. They are full of pincer-movements on the Western Front and waves of Norsemen assailing the coasts of Britain, etc.
For day 2, he covered a few pages with numbers, attempting work out what a completely impossible fraction-of-a-fraction-of-a-fraction (that he made up) would equal as a decimal. This is NOT something I would have ever done as a kid, but he will regularly do this, while whistling, singing or just beatboxing. I think he enjoys the feeling of having his brain fully engaged in something. People going past admired and said "Wow, he's a bit of a genius isn't he?" One said "Goodness, is he .. doing homework???"
Leaving aside the fact that our other son, the strapping right-fullback, is also a mental wunderkind, the fact is Michael's numbers actually made no real sense, but he was as happy as a trout. For us the big thing is we can take him off to something like the soccer carnival, and he keeps himself occupied one way or another, despite his zero interest in soccer.
There has been a bit of a sportfest at home lately with footy and soccer on TV every other day. While Marcus and I are absorbed in that stuff, Michael is on the floor between us and the TV, with anything from 3 to 10 books open all over the place. Library books and my books, his books, old books that i can't remember where they come from. And he takes a bit from here and a bit from there and makes something new. These below all come from a 4-5 day period, except the map of France at the end. That was a sustained effort over about 4 days, drawn on an x-ray envelope.