Dramis

The way-side shrines and the eaves of houses in Bhutan are often decorated with "drami" or good luck symbols. These are found in many Buddhist communities. They are continuous single line designs, an idea that is also found in Celtic knots in Europe, Rangavali doorstep patterns in India and in the sand drawings of Central Africa.

Can you draw these in one continuous movement?

Creating Drami

One simple way to create Drami patterns of any level of complexity is to start with intersecting lines. The diagram below shows how the third level Drami can be constructed by first drawing three lines vertically and horizontally. The corners of alternate pairs of ends are joined to complete the Drami.

Investigating Drami

If you create Drami of different sizes it is interesting to investigate the number of squares in each and to try and relate this to the order of the Drami (the order of the Drami is determined by the number of horizontal/vertical lines).

For example the first level Drami has two squares, the second has 5 squares

Order of Drami	1	2	3	4	5
Number of Squares	2	5

Now see what happens with higher order Drami and see if you can find a pattern or relationship.

Extending the Investigation

An extension of this investigation is to create Drami so that the number of vertical lines and horizontal lines we start with are not equal. Here for example there are 2 horizontal lines and 3 vertical lines.

Now create other Drami with an unequal number vertical and horizontal lines and try and find a relationship with the number of squares.

Horizontal Lines

Vertical Lines

Number of Squares