Doodle God is a badged puzzle game on Kongregate that gives you the reins to creation and tasks you with creating 115 total elements from a starting pool of just four. An iOS version of the game has also been released. There is a counter-part to the game called Doodle Devil.
In the start of the game, players are presented with the four basic elements. The object of the game is to combine these elements in such a way that they create new elements. Click on an element to select it, then click on another to try to combine them; if they don't mesh, nothing will happen, but if your matchmaking works, you'll have a whole new element to play with. The goal of the game is to find the combinations to create all 115 elements in all 14 groups. The iOS version has 140 elements to discover.
The game has its own quirky sense of logic and the combinations are seldom obvious. Since this pushes the gameplay into pure guessing, it can be considered a Brute-Force puzzle. Thankfully, the game has a hint system. Every 3 minutes, you can click a glowing lightbulb and get a hint which reveals 2 groups which have elements that can be combined.
Walkthrough for all 140 elements.