I have always tried to encourage my DD to have an "inner world" (for want of a better word) by letting her find her own entertainment (using whatever she would like that is available around her) rather than structuring her play.
As a result, at 4.4, she makes a lot of mess can amuse herself for hours on her own, talks to herself a lot and is great on imaginative play. Her very favourite playmate is her first cousin, my sister's daughter, who is very much on the same wavelength and the two little girls can play together for days without interference or entertainment from adults.
Sadly, my niece lives in another country so the two little girls don't see one another that often.
The upbringing my DD has is, however, very different from most of the children around us and she isn't on the same wavelength as the children in her class at school.
How have you developed your children's inner world? Are parents/children around you on the same wavelength or not?