One effect of nested patterns is that the specified scale factors or rotations can be cumulative. For example, if one pattern contains a reference to another pattern, and the reference scales the pattern, as shown below:

 

pattern A is

    scale 2:1 pattern B

 

then pattern A is pattern B at twice the size at which pattern B was defined. If you then specify:

 

pattern C is

    scale 2:1 pattern A

 

then pattern C is actually pattern B, doubled in size to become pattern A, then doubled in size again to become pattern C.

 

The following examples illustrate the effects of scaling and rotating patterns. Take particular notice of the position of the pattern's reference point and of any effects of accumulation of the scale and rotate specifications. These examples use the two patterns defined below:

 

screen size 1200 900

 

pattern Box is

    white shape       # Box

        boundary

        draw 300 0, 0 150

        draw arc 90 degrees center by -50 0

        draw -250 0, 0 -100

    end shape

    solid white shape    # Door

        boundary

        draw -10 0, 0 190, -10 0, 0 10, 20 0

    end shape

 

pattern Flag is

    solid red shape

        boundary

        draw 10 0, 0 160, 40 0, 0 40, -50 0

    end shape

 

The first pattern is a mailbox. The second pattern is the red flag seen on mailboxes. The pattern defined below contains a reference to each of these patterns:

 

pattern Mailbox is

    pattern Box

    move 100 80

    pattern Flag

 

Mailbox is displayed as shown below. The reference point for the pattern is marked.

The following are illustrations of transformations on these patterns.

 

scale 2:1 pattern Box

 

pattern MailArrivedBox is

  pattern Box

    move 100 80

    rotate -90 pattern Flag

 

The following pattern definitions:

 

pattern BigBox is

    scale 2:1

    pattern Mailbox

 

pattern TippedBox is

    rotate 30

    pattern BigBox

 

contain an example of a nested pattern. The first pattern, BigBox, consists of a scaled version of Mailbox. The second pattern, TippedBox, consists of a rotated version of BigBox.

 

BigBox looks like this:

 

It is the pattern Mailbox shown at twice its size. When TippedBox is displayed, it is a rotated version of BigBox, as shown below:

 

 

If you then define:

 

pattern SmallBox is

    scale 1:2

    pattern BigBox

 

BigBox is Mailbox scaled to twice its size, and SmallBox is BigBox scaled to half its size. Thus, the pattern Mailbox is displayed in the size at which it was initially defined.