I am building a puzzle game using only geometric shapes and a simple "flat" design (see screenshots). So far, I've build the prototype in Processing (Java), but now I'd like start building it for real. My requirements:

• Be able to run the game on (at least) iOS and Android
• Draw the shapes programmatically (i.e. vectors, no bitmaps)
• As little learning curve as possible to adopt new platform
• I don't need fancy features (like multiplayer, 3D, genre-specific boilerplates or level builders)

Which game engine or programming framework would you recommend for this purpose?

There are many tools that can help with that.

GameMaker:Studio and GameSalad immediately spring to mind.   So do libGDX, Cocos2D-x, Marmalade, and Corona.  Then there are tools like Construct, App Game Kit, Love, JMonkey, ClickTeam Fusion, and on and on.  Even Flash is an option.

Use your favorite search engine, see what tools suit your fancy and can easily produce games like the ones you are presenting, and try them out. Nearly all the good ones are at least free to try if not completely free for the size of game you're discussing.

For simple project I'd recommend to use LibGDX. I've worked with it few tears ago. Even have published tutorials on github.

You can find here complete source of my version of Bomberman.

As long as it's simple game maybe it's better to use standard canvas (android) https://developer.android.com/reference/android/graphics/Canvas.html, for ios there is definitely an equivalent? I don't see a point of using any specific game framework for this kind of game.

1 minute ago, RootKiller said:

As long as it's simple game maybe it's better to use standard canvas (android) https://developer.android.com/reference/android/graphics/Canvas.html, for ios there is definitely an equivalent? I don't see a point of using any specific game framework for this kind of game.

Framework allows you to make cross-platform game. With canvas from native SDK you have to make it independently on each platform.

Personally I will never use any kind of pre made framework for such a simple game as OP has. A lot of frameworks will take thousands of bytes just to setup stuff you will never use. You can always write game logic in some higher level language such like lua if it gets complicated. Still imho for this kind of game it's the best to have it wrote as low as possible.

Libgdx, for example, pretty lightweight. Last time I'v worked with it, it has added less than 1mb to result apk.

Thanks for your thoughts. I had a look at a range of the suggested options from @frob and was optimistic about Libgdx, but found out that the drawing functions were very limited. Things like a good-looking stroke did not come out of the box. I want to focus on development and not graphics rendering, so I looked on.

Instead, I'm currently trying to implement using SVG in Javascript (using svg.js library for convenience). It creates a nice fast workflow, even though I'm not so handy or happy with JS. The next step will be to see how to make it into native apps, using a webview and then putting (as few as possible) native features around it.