Wall Paper tiling covers an area with a repeating patterns and there are many possible ways (seventeen) to repeat a basic design called the "Seed" or the motif. In this class we will explore some of the seventeen possibilities.

One method to create a wall paper periodic two dimensional designs uses the TILE command.  Typing TILE [CIRCLE 40] will cause the whole screen to be covered with circles touching each other.  In a similar way typing TILE [BOX 50 50] will cause the screen to be covered with squares.   The tile command computes the dimensions of the basic motif and spreads it around the screen in a regular manner.  Sometime it is necessary for the human programmer to define the actual area to be tiled.  For this purpose the TILEWH command is used.  For example:  To tile the screen with circles which are spread out a little you can use:
TILEWH 40 40 [CIRCLE 30].  If you want then to touch horizontally, the command TILEWH 40 30 [CIRCLE 30] will do.

Questions:

1.  Write a program that produce a picture similar to this one:

2.  Use the BOX 40 40 command and the TILEWH command to create this picture.

3. Write a program that produce a picture similar to this one:

4.  Create a similar design as the one below.

To create a design similar to this one: (Hint use TILEWH and spin a line around the center)

5.  First  create a basic pattern that looks like this:

then use it to make a chessboard tile: