sona chowk

One part of myself has fallen in love with the sona drawings (http://www.ikolam.com/node/6485
http://www.ikolam.com/node/6528
http://www.ikolam.com/node/7021)
As long as the numbers corresponding to the rows (R) and columns (C) are relatively prime (that means they do not have any coomon divisor) we get one single line that surrounds all the dots. But if these numbers have common divisors, then we get more than one line depending upon the numbers. What I did something novel (I haven't seen this described anywhere as far as I know) is to form a square from the sona drawings. This square too has some interesting properties. It looks that when we have a single line in the sona drawing, there are two lines in the sona square. But if the number of lines in the closed sona drawing is more than one, then the number of lines in the sona square too is more than two and varies according to the number of rows and columns. These sona squares serve as very good borders for other rangOlis. Actually I tried this method for a rangOli of mine which you'll see in due course. I am enclosing a picture that gives an array of representative sona squares along with the sona drawings. The R and C are the rows and columns and the first value of N is the number of lines in the original sona drawing and the second number is the number of lines in the sona squares I created. These are all chikku kOlams in our parlance and can be constructed with a string with up and down and in and out motions. I want to call the sona square as sona chowk!

Regards! - mOhana