How simple is it, to see chaotic behavior emerge. You just need to look at a double pendulum (http://scienceworld.wolfram.com/physics/DoublePendulum.html). A single pendulum follows a predictable pattern – back and forth maybe around the center point if you swing hard enough. Attach a second pendulum to the end of the first and unpredictability ensues. Suddenly, the trajectory of the end point is erratic and varies wildly with small changes in the initial conditions.
To understand how within chaotic behavior, still patterns exist, you again look at the double pendulum. Attach a pencil to the end for it to draw on paper where it goes. Even though the end point swings in all sorts of directions, all the swings leave a space open in the middle.