A frieze pattern is a decoration made from repeated copies of a basic unit, arranged in a row. Figure 1 shows an eleventh century example in the Islamic Art section of the Metropolitan Museum of Art.

a.Provide a top-level decomposition of the problem of drawing a frieze pattern, assuming for the moment that the basic unit is repeated just six times.

At this stage you are not trying to produce a solution, just break the problem itself down into smaller parts. We are looking for a ‘bird’s eye view’ that could apply to a frieze composed of any basic unit. For now you should just assume that the exact form of the basic unit will be considered later, so you can just say ‘draw basic unit’ for that step.

Your initial decomposition should use exactly one loop.

(4 marks)

In the remainder of this question, you will design and implement a program to draw the particular frieze shown in Figure 2.

The figure shows the detail of each star, and the distance between successive stars. The acute angle interior to each point is 20 degrees. The lines that form the edges of each point are each 30 units long. The exterior angle formed where each point is joined to the next is 110 degrees. Finally, each star is shifted 100 units to the right relative to the previous star.

Hint: you will probably find it easiest to think of each star as being built of four ‘elbows’ shaped like the one below, with the first one being angled at 10 degrees to the horizontal, as seen in Figure 4. After drawing each elbow, a rotation of 70 degrees right will ready the turtle for the next elbow.

  
 
 
 
 

Figure 1 Example frieze