Polygons Square
Playing turtle
Let’s get you or someone else to walk in a square like a turtle using the commands forward and right or left. You know the a feature of squares is all sides are the same length. Another feature is all corners are made by turning the same number of degrees.
In walking, we can decide on the number of turtle steps. We can easily approximate the turning angle if the room we are in is either square or rectangular. We just turn enough to face the adjoining wall. To come back to where we started we have to make four turns.
Okay now let’s see how we translate our behavior back to the turtle.
Playing with Turtle
We can decide on the length of each side by giving the turtle different forward instructions. To see the assorted lengths remember to put the pen down
pd
then try out different fd instructions
fd 5
eek! too tiny.
fd 20
still to small
fd 85
great!
The amount the turtle turns is not open for discussion. It is constant and computable. Remember how many degrees we turn to get back to the same heading as we started. A full circle contains 360 degrees. We have to complete a full circle in making a square. Remember we turned the same amount four times. So now we have the solution. We divide 360 (the total amount) by 4 (the number of corners) and the result is 90.
The first part of the turtle’s trip is
fd 85 rt 360 / 4
and we repeat those instructions three more times.
fd 85 rt 360 / 4 fd 85 rt 360 / 4 fd 85 rt 360 / 4
Now let’s turn these instructions into one by writing a procedure.
I’ve chosen square as the name, but you can choose another name.
to square
Now as programmers we can choose how to write the instructions. For example we can just copy the four lines and let them be the procedure.
fd 85 rt 360 / 4 fd 85 rt 360 / 4 fd 85 rt 360 / 4 fd 85 rt 360 / 4
or we could decide to use repeat in the following way:
repeat 4 [fd 85 rt 360 / 4]
Notice repeat takes two inputs: the number of times an action is to be done and the action to be taken. The second input is a list and so is enclosed in square brackets.
To finish the procedure off the final line is
end
So either
to square fd 85 rt 360 / 4 fd 85 rt 360 / 4 fd 85 rt 360 / 4 fd 85 rt 360 / 4 end
or
to square repeat 4 [fd 85 rt 360 / 4] end
should work. But before going any further try your square procedure out. Check for bugs.
Here is a video of getting the turtle to draw a square.
Later I chose to write the square procedure as
to square repeat 4 [fd 85 rt 360 / 4] end
I tried it by typing into the command center my new instruction.
square
Aha! I’ve taught Logo a new word.
Applying What I Just Learned.
I can play around a bit with my new procedure.
For example, I could make
What does the turtle do differently in the two designs?
In one the turtle turns right between each square and in the other the turtle turns left.
Try inventing other designs such as a square that looks like it was made up of four squares.
Make the turtle draw a large square made out of four smaller squares like
Applying a Turtle’s Pen Features to Square
A turtle has a position on the screen, a heading, and a pen. The pen has a color and a size (width). Let’s explore some pen effects.
What’s the widest size the pen can be? (Just try different numbers until the error message tells you what that number is.)
The pen size is 1 at the start.
setpensize 10
changes the width to 10 turtle steps wide. The result is
Now let’s change the pen color.
setc “red
or
setc 15
repeat 4 [square rt 360 / 4]
results in
By the way, in my first try at doing this I made the first square smaller than the other. I didn’t panic. Instead I thought about how I could use that bug.
The way I did this not take advantage of changing the square procedure to take an input and thus be able to draw different sized squares.
Here’s what I did:
repeat 4 [square rt 90] repeat 4 [repeat 4 [fd 50 rt 90] rt 90]
If I change square to
to square :side repeat 4 [fd :side rt 90] end
then I can say
repeat 4 [square 85 square 50 rt 90]
I could change the pen color in different places.
A cute trick is to use random. The command, setc, can ber given either a number or an alphabetic name. Using numbers we can get a new color randomly. The number of different colors is 256 (0 to 255).
So setc random 256 is the magic instruction.
And now combining pen color and pen size we can make unusual designs using square. For example
is one result from running design2 rt 45 design2.
to design2 setc random 256 setpensize 10 repeat 4 [square1 100 square1 50 rt 90] setpensize 5 setc random 256 repeat 4 [square1 100 square1 50 rt 90] setpensize 1 setc random 256 repeat 4 [square1 100 square1 50 rt 90] end
Here is another result from dazzle, the procedure listed below. Enjoy changing it.
to dazzle pd setpensize 30 setc random 256 repeat 8 [square 100 rt 45] setpensize 15 setc random 256 repeat 8 [square 100 rt 45] setpensize 7 setc random 256 repeat 8 [square 100 rt 45] setpensize 1 setc random 256 repeat 8 [square 100 rt 45] end
Notice dazzle makes eight squares turning 45 degrees between each square.