I recommend doing this in a vector program. For my demo I am doing this in Illustrator.
Draw the background square.
Draw some paths that will separate the square.
I then gave the paths a stroke and stroke width of 4. Pick a number for how much space you want from each object. I then selected all of the strokes and went to Object -> Expand, and expanded the stroke.
Select both the strokes and background and open the pathfinder options, Window -> Pathfinder and select "Divide".
Select the black stroke with the direct select tool and go to Select -> Same -> Fill Color and delete all of the black fills.
In Illustrator CC, select all of the blue objects and use the live corners to make the corners round.
In Illustrator CS6, and below, select all of the blue objects and go to Effect -> Stylize -> Round Corners.