With the 3 points Adaptive Component creating a quarter of ellipse sweep as described in . . . Ellipse . . . Points, a pattern of overlapping ellipses or circles (circle is an ellipse with equal axes) can be easily created.
Curtain Panel Pattern Based
Nest the 3 points ellipse sweep family into a curtain panel pattern based family. Parameterize length 12, 23, 34, 41 as reporting parameters L12, L23,L34 and L41 respectively. Place the ellipse sweep family by snapping on point 1, point 2 and point 4. Continue placing instances by 3 points: point 2 point 3 point 1, point 3 point 4 point 2, point 4 point 1 point 2.
Select all the ellipse sweep family instances, associate the sweep radius parameter R with parameter R in the host family. Put a formula for parameter R so that it will change with the module size of the curtain pattern.
Now the curtain pattern family is ready to use.
Pattern on Surface
By creating surfaces, dividing them and mapping the curtain pattern family, the popular Islamic pattern of ellipses or circles overlapping can be made.