Expansion costs increase fairly rapidly, going up every one or two expansions, although the exploration time seems to be constant at 4 hours. (Update: On Android, initially it seems to be expansion costs double every expansion and exploration time is 2 hours per block. Further Update: Change point to multiple blocks per price level and the exploration time to 4 hours per block happens at block 8 - 448 coins).
The entire Island Map is broken into a 40x40 'area' grid, with each of these grid squares consisting of a 5x5 'land' grid. Most merchants require a 4x4 space and most houses require a 3x3 space, please see individual pages for exact space requirements.
There appears to be an additional constraint in placement of buildings (houses, merchants and decorations) in that a "walkway" connecting all open areas of land must be maintained for your population to roam around in. So while it may appear possible to place a building on in an open place, if this placement would result in no open pathway remaining, the placement is blocked (TPC will not permit you to place the building).
Each time you expand you discover one area grid, unless it is immediately surrounding one of the fetaures. When you uncover a feature you get 4 area grids (10x10 land squares) for the price of one to allow for the fact that a 4x4 section is occupied by the feature!
Note: Not all 25 'land' squares in a grid need to be actual land. On the island edges any number can be water.