Doodling can be lots of fun. Squiggly checkerboard circular (curved) doodles are easy to draw. Option 1
: Start by drawing a standard checkered board. Then draw closed shapes (circles, ovals) on top of the checkerboard. Be sure to avoid drawing lines over corners. Option 2
: Simply draw a circle over another circle; avoid drawing a new line through an intersection of existing lines. The result is a perfect checkerboard full of shapes. Never draw a line through a point where two other lines cross.
Once you've finished, you can color it in! Check out an example here