Don't print this page. You can read it from the screen as you follow the steps.

1. Find and execute the program recPic.dem.
2. Select <Examples:face>.

A face should appear on the left hand side. It is a figure specified by a set of lines, circles, and arcs and by two points that are referred to as the "handles". The handles are the two red dots. Note where they are located with respect to the face.

3. Select <Mode:Draw or Handin>. Select the circle for "n=base=1".
4. Draw a face on the screen as follows:

Press the left mouse button down in one location. Continue to hold the button down while moving the mouse. Lift the button in a second location. Note where the face gets drawn with respect to where you press and release the mouse button. The figure of the face is translated, rotated, and scaled so that the two handle points of the figure land on the two points that you have specified.

5. Draw a few faces in different orientations and different sizes.
6. Clear the screen when you like by selecting <File:clear screen>.
7. To try something else, select <Examples:recur1>.

A rectangle should appear on the left, with the handle at the top edge of the rectangle. On the right, a rectangle with an arrow pointing pointing down towards the "recurse" arrow "---> >---". Note that the handle at the top edge of the rectangle.

8. Select <Mode:Draw or Handin> and again be sure that the circle for "n=base=1" has been selected.

When "n=base=1", the figure that is on the left hand side is drawn. When "nonbase", the figure on the right is drawn.

9. Draw a few rectangles in different orientations, then clear the screen <File:clear screen>.
10. Click in the circle for the button <nonbase> and draw a big copy of the "rectangle with arrows" (the right hand picture in point 7) by clicking the mouse as before -- have the top of the rectangle be close to the top of the screen about 1/2 of the width of the screen.
11. Draw a smaller copy of the "rectangle with arrows" at the place to recurse -- the arrow "---> >---" specifies a "place to recurse".

Hold down the mouse button at the beginning of the arrow, i.e. "x---> >---", move the mouse to the end of the arrow, i.e. "---> >---x", and lift up the button.

A smaller "rectangle with arrows" with a smaller place to recurse arrow is pointed to by the first (and larger) rectangle.

12. Draw a smaller copy of the "rectangle with arrows" at the new place to recurse.
13. Repeat this process, drawing smaller and smaller copies.
14. Eventually, you will want to stop. However, you do not want to leave a "place to recurse" "---> --->" without a figure. Therefore, select "n=base=1" and draw a rectangle at the smallest place to recurse.

You have drawn a "recursive picture". recPic.dem draws such pictures automatically. A recursive picture is specified by a "base case" figure, a "nonbase case" figure, by a set of "places to recurse", and by an integer "n". The base case figure is shown on the left hand side of the Edit Mode screen. In this case, it is the rectangle. The nonbase case figure and the places to recurse are shown on the right. The places to recurse are specified by an arrow. In our present example, the nonbase case figure is the "rectangle with arrows",and there is a single place to recurse. The value n is selected with the circle radio buttons on the right of the draw screen.

A recursive picture is drawn as follows. If n=base=1, then the base case figure is drawn. If n>1, then the nonbase case figure is drawn. As well, the location on the screen (specified by two points) of each place to recurse is determined. Then recursively the same picture is drawn at these locations but with the value n-1.

The best way to understand this is to try it with larger and larger values of n.

15. Clear the screen and click the button <n=2> and draw a figure.

With n=2, the "rectangle with arrows" is drawn. Then at the one location to recurse the recursive picture for n'=n-1=1 is drawn. Recall the n=1 picture is only a rectangle (no arrows). Therefore, the rectangle is drawn at the place to recurse. Remember what the n=2 picture looks like.

16. Click the button <n=3> and draw a figure.

Again the "rectangle with arrows" is drawn. Now, however, at the place to recurse, the n'=n-1=2 is drawn (the previous picture). Remember what the n=3 picture looks like.

17. Click the button <n=4> and draw a figure. 

Now the n=3 picture is drawn at the location of the first place to recurse.

18. Try other values of n.
19. Now repeat the process with other recursive pictures.

Open <Examples:three>. Note what the base and the nonbase case figures are. Go into edit mode and select <nonbase>. Draw a big copy of the picture. Then in each of the four places to recurse draw a smaller copy of nonbase case figure. This produces 16 places to recurse. Again draw an even smaller copy at each of these locations. Repeat this until you get the idea. In order to stop, select <n=base=1> and draw the base case figure at each place to recurse.

Clear the screen and have the program draw the recursive picture. Start with n=base=1. Then n=2, n=3, ... . Each time remember what the previous picture looks like. Then for the next value of n, note how the nonbase case picture is drawn, however, in the "places to recurse" the picture for n-1 is drawn.

20. Repeat the process again with the other examples listed.
21. You are now ready to create your own figure. Select <File:new base/nonbase>. Add lines, circles, and arcs to the base and the nonbase case figures and places to recurse to the nonbase case figure. Then select <File:Draw> to see the result. Read the help file for for further help.

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