sOna Patterns - New Insights

I have already displayed this pattern in a different manner at http://www.ikolam.com/node/7066?p=1930 I reworked on this again in two different ways and am presenting it in this blog. I hope this is a bit educational. This pattern has ten rows of dots and eleven columns of dots (larger ones). These two numbers are relatively prime, that means one is not divisible by the other (11 is not divisible by 10 to give a whole number). So the pattern is a chikku kOlam with one string (on the left). You may very clearly observe the up-and-down motion. The picture on the right is the same pattern, but coloured in a different way. I will discuss the significance of this picture. Two numbers n and (n-1) are always relatively prime. That means a number and another that is one less (or more) than this are relatively prime, that means n can not be divided by (n-1). The only trivial exception for this is 2 can be divided by 1. This pattern done with 11 and 10 dots has this property. If one reduces these numbers repeatedly by 1, we get 10 and 9, 9 and 8, 8 and 7, etc. till we reach 2 and 1. In the right pattern the sOna pattern for all these combinations are present. Each colour belongs to a particular combination. While white is for 11 and 10, blue is for 10 and 9 (with the smaller dots), orange is for 9 and 8 (with bigger dots), etc. till we reach the trivial case of 2 and 1 at the centre. Therefore there are ten sOna patterns in this. For those who may be wondering how I am able to get the up-and-down motion of the lines, first I draw lines in the usual way with various lines crossing each other. Afterwards, for the lines going below, I cover using white straight lines of proper thickness on either side of the crossover point. This has to be repeatedly performed. Yes, it is very very stressful to the eyes. Finally, some crossover points have to be retouched with the proper colours. Afterward, to get the rangOli powder feeling, I apply the noise-spread technique and take a negative if I desire a black background as in these pictures. Hope you enjoyed this writeup. Regards! - mOhana