I would try to do something new, or get started on something you've always wanted to do. Do you have any dreams or aspirations that have fallen by the wayside? Now's a good time to pick those up again. Also I would suggest really trying to work on yourself, maybe try facing some of your fears. And just keep trying new things, if they don't work, don't worry about it, just brush it off and move on to the next thing.

Maybe I'm like your ex in that I'd prefer to have space after a relationship too. I wouldn't be opposed to having a friendship down the line but for the first while I think space is important so that the two of you can move on with your lives. Perhaps he feels the same as me and maybe just didn't explain it to you? I generally think the more time I spend with my ex-partner after a break up the harder it becomes to accept the break up. The point is to give time for you both to move on, become stable on your own first, then think about being friends again. Anyway, I don't know if that's the case but maybe that can help you to understand why he might want his space right now.