How to create new designs

Here is a 6 x 6 dot pattern (or 1 to 11 straight diamond). With a dot pattern like this, if we join in the usual way, we will get six lines (please draw it and convince yourself that it is so). What I did here was - I drew purple lines through orange dots like the two sides of a right angled triangle. These lines are like walls (or mirrors). When we draw lines around the points, we cannot penetrate these walls. With this type of restriction, we get only two lines (the yellow and pink). Please note that the walls themselves are placed in a symmetric fashion obeying four-fold symmetry (90 deg rotation). By erecting these walls at different places, we can get different designs with different symmetries and different number of lines. For a given set of dots, one can thus design a large number of patterns.

Regards! - mOhana