If there is one thing we can all agree upon, its that a child's imagination has no limits. If you want to stimulate your child's mind from a young age, you should have him do creative things, and a digital coloring book would be the right choice.
One example of a good coloring book is Color Island (Free).

Even if your child is left unattended and he manages to open the app all by himself, the menu is so intuitive that he will have no problem navigating in it on his own.All you have to do is select what category of pictures you want to start coloring and select the desired image. 
Once you pick your image, you will see the drawing tools you have at your disposal: several brush types, an eraser, a color filler,  a palette of almost 50 different colors and the option of modifying the brush size.

One neat feature that we found was that the color filling tool cancels out all the brushes previously applied in an area. This makes it easier to fill out large blank spaces in case we ever tried to do it by brush and failed.Considering how children aren't the steadiest of hand, it's a welcome feature.
Considering how this app is aimed towards children, the available tools are more than enough to satisfy even the pickiest toddler.

Color Island (Free) is not just about fun and games. Two of the tabs also have an educational purpose, such as the alphabet tab where you can color, and learn the whole alphabet, and the number tab where you can color and learn all numbers between one and twenty.

If your child is more advanced he may try to use the "Color by number" tab, where all pictures are color coded so that your child will always know which colors to properly use. This is in no way a restriction as he can still use whatever colors he wants.

Color Island (Free) boasts a simple UI, fun drawings and a wide array of tools, making it a good alternative for when you want to keep your child busy and entertained for hours on end.