A type of chikku kOlam explained

Today I want to explain how we can draw a chikku kOlam and expand it to as big a size as one wants. The basic motif is a simple 3x3 dot motif as shown in Fig. (a). This is indeed a chikku kOlam as shown in Fig. (b). Now five of these 3x3 motifs are placed as shown in Fig. (c). We now get a 7x7 dot chikku kOlam that has only one line. This particular pattern done in my own way with up-and-down weaving motion will be uploaded and displayed in the regular rangOli section. Five of these 7x7 motifs can be placed in the same way as in Fig. (c) to obtain Fig. (d). This has 15x15 dot motif. Again five of these can be built in similar fashion to give rise to a 31x31 dot single line pattern as shown in Fig. (e). One can go on building in this fashion ad infinitum. By the way, the next pattern will have 63x63 dots. The dot count for these kOlams are 3, 7, 15, 31, 63, 127, etc. given by the general formula (2^n - 1) and such numbers are known as Mersenne numbers. Many of you may be familiar with these rangOlis rotated by 45 deg. I have also formed a sOna square with the 7x7 pattern which, as expected, yields two lines.

Regards! - mOhana