In the first post on Cistercian Numbers, I covered drawing the Cistercian numerals zero through four using ucblogo (Berkeley Logo). Five was left as a future exercise with the point that it’s possible to think of five as the result of combining drawing both four and one:

In this post, we’ll dive into an approach to drawing certain numerals as combinations of other numerals.

To describe the challenge in a bit more detail – if the commands for drawing four and one are simply run one after the other:

TO Draw.5
  Draw.4
  Draw.1
END

The result is interesting; but, it is not the numeral for five:

In order to layer the two numerals properly, we need a way to reset the turtle’s position between drawing the two numerals:

The approach taken in this post is to write two new commands – Save.Turtle and Restore.Turtle.

The Save.Turtle command will save the turtle’s position and heading. We’ll call this prior to drawing the first numeral so the turtle remembers where it was before drawing anything. This way, the turtle can return to its starting position and heading from any other position and heading on the screen:

To Save.Turtle
  MAKE "Saved.Turtle (LIST POS HEADING)
END

Walking through the code:

• POS – outputs the turtle’s current position
• HEADING – outputs the turtle’s current heading in degrees.
• LIST – outputs a list, with the turtle’s position as the first member and the turtle’s heading as the last member.
• MAKE – assigns the above list value to the variable named Saved.Turtle

The Restore.Turtle command will go back to the saved position. We’ll call this prior to drawing any additional numerals. This way, the numerals will draw precisely on top of each other so they combine as expected:

To Restore.Turtle
  PU
  SETPOS FIRST :Saved.Turtle
  SETHEADING LAST :Saved.Turtle
  PD
END

Walking through the code:

• PU – lift the pen, so the turtle does not draw while moving
• FIRST – outputs the first member of the list Saved.Turtle
• SETPOS – moves the turtle to the position returned from FIRST
• LAST – outputs the last member of the list Saved.Turtle
• SETHEADING – turns the turtle to a heading in degrees returned from LAST
• PD – puts the pen back down, so the turtle will draw when next moved

A possible improvement here would be checking if the pen is up or down using PENDOWN? before calling PU and then restoring the pen to its original state rather than always calling PD.

Now, we can draw the numeral for five thusly:

TO Draw.5
  Save.Turtle
  Draw.4
  Restore.Turtle
  Draw.1
END

This is a good breakpoint as the numeral for six is a new base shape. In the next post we’ll teach the turtle to draw six, we can teach it to draw seven, eight, and nine using the numerals for six, one, and two: