Expansion of the city is tightly managed. Only a certain number of industrial buildings can be added until the population reaches a threshold. To offer constant city re-development, buildings aren't fixed in place, but can be dragged to new plots.
Your chance to play as Caesar comes in The Settlers (£2.99, iPhone; £2.99 iPad). A free version is available as a taster, and it's more palatable than most thanks to the absence of IAP.
The Virtual City series leans more towards detailed infrastructure planning and resource harvesting, lending it a shade of old PC favourites such as Transport Tycoon, though erecting buildings is part of it as well. It's more heavily structured by its level-based approach: after completing one, you'll often find yourself transplanted to another one to help raise its economic game.
Growth is achieved by establishing production chains. Once key buildings - such as a mill and a bakery - are in place, you buy trucks and assign routes for them to carry resources along the chain. There's also housing and public transport to consider, and refuse to clear, so a city isn't inundated with waste.
Virtual City (iPad, £2.99) is available in this full version, or in a free version, with a few levels as a taster, and the full game unlocked through IAP. This game includes a sandbox mode, but that's developed on in Virtual City Playground HD (Free, iPad). It takes place on one landscape, and while it's more of a sandbox overall, the city limits are restricted at the start; goals have to be followed in order to raise capital to expand them.
EA makes another city-building game for iOS besides SimCity. The backstory behind The Simpsons: Tapped Out (Free, Universal) involves an explosion at the nuclear power plant, leaving Homer to recreate Springfield. With successful missions, he discovers fellow cast members and their respective businesses.
A social element introduces a multiverse of different Springfields run by other players, which you can visit to take limited amounts of income from them daily. Characters can be assigned tasks to earn cash derived from their personality (Homer can lounge in the pool, or Lisa play the sax), though they take real time (in some cases, hours) to complete.
Notification Center is used to tell you when a character is free to take new orders. Things can be hurried along by spending donuts, which are quickly acquired through not-so-delicious IAP. However, fondness for the characters is encouragement to play the slow game.
The Wizard of Oz Game (Free, Universal) roughly follows the film's narrative, and reuses imagery and audio from it. Starting out in Munchkinland, you're tasked with growing the population to help you build the Yellow Brick Road so you can meet the Wiz and get Dorothy back to Kansas.
Tap Paradise Cove (Free, Universal) has a tropical island for a setting. Placing buildings isn't as simple as choosing where to erect them. You have to harvest the resources for construction. Yes, you'll holler 'IAP ahoy!', but there's action to be had too, in which you build ships to protect your bounty from nasty pirates.
Finally, for a burst of nostalgia, hardcore Sim fans might enjoy Yoot Tower (£5.49, iPad), where you're charged with growing a skyscraper packed with offices, condos, hotel rooms and more, ensuring people have everything they need.