Logo Tutorial

History

Logo was developed in the late 1960s at Bolt Beranek and Newman, Inc., in Cambridge, MA by W. Feurzeig, D. Bobrow and S. Papert. Its purpose was to teach children to program. Its central feature is that it provides simple commands for moving a ``turtle'' on a surface. Initially the language was used to direct the motion of a small robot that was dressed up to look like a turtle. It was placed on a sheet of paper and dragged a pen underneath it, thereby drawing figures on the paper. Today the ``turtle'' is a small arrow-like figure that moves on the screen of a computer.

Underneath, Logo is very much like Lisp, the list-processing language used in Artificial Intelligence, the branch of computer science that tries to make machines behave intelligently. However, it also has features of other languages, including Pascal.

The Logo Environment

The Logo in use at Brown is Berkeley Logo. It can be activated by selecting it from the left Menu button. You will have to position a window on the screen. We will call it the command window. Another window will appear, possibly on top of the command window. If necessary, use the middle mouse button to move it (drag the top of the window) so you can see the command window again. A ? prompt is presented in the comand window. At the prompt, commands can be issued that are executed immediately. When a drawing command is issued, say, the command forward 10, a graphics window appears which must be positioned on the screen. The graphics window in this case shows an arrowhead (the turtle) with a line behind it that is 10 units long. When other drawing commands are issued, such as rt 45 fd 60, the turtle turns right 45 degrees and then advances another 60 units. The command cs will clear the screen and reposition the turtle at its center.

Sometimes you will need to stop a Logo procedure. Do this with ^c (control c). To exit logo, type bye in the command window.

Logo the Language

This tutorial provides the rudiments of the language, enough to do the simple assignments that are given in CS4. The commands that we explain are drawing

commands, variables, arithmetic operators, and procedures, including recursive procedures.

Drawing Commands

The simple Logo drawing commands move the turtle forward and backward and turn it right or left. The commands and their abbreviations are given below:

fd forwardbk backwardrt rightlt leftcs clearscreen

Either version of these commands can be used.

Each of these commands must be followed by one value called its argument. The arguments for fd and bk are units; those of rt and lt are angles which can be any integer. Of course, a rotation by 360 is a complete rotation so a rotation by 375 degrees is the same as one by 15 degrees.

The graphics window has a coordinate system. The values of the two coordinates (normally called x and y) at the center are 0, 0. At the northeast corner they are 250, 250; at the southeast corner, they are 250, -250; at the southwest corner, they are -250, -250; etc. If the turtle tries to walk off one side of the screen, it wraps around. The right side wraps to the left side and the top wraps to the bottom.

Now let's try some commands. Commands be issued one per line followed by a carriage return. Several of them can be typed in succession in a command window followed by a carriage return. The effect on the turtle is the same. However, if you type a command that requires one or more inputs and provide the missing input(s) on the next line, Logo will complain.

The commands

fd 60 rt 120 fd 60 rt 120 fd 60 rt 120

cause the turtle to draw a triangle, as you can see by trying them out. These commands are read from left to right. Since the command fd requires one argument, it is taken as the next value. Similarly, rt takes one argument also. Thus, Logo can give unambiguous meaning to each of these character strings. For some Logo commands separators are needed.

In the above example, the commands fd 60 rt 120 are repeated three times. To save time and space Logo provides the repeat command. The following command has the same effect as those given in the above example.

repeat 3 [fd 60 rt 120]

The square brackets indicate that the enclosed commands are to be executed three times.

Other Turtle Moving and Drawing Commands

Logo has a number of other drawing commands, including those shown below.

pu penuppd pendownht hideturtlest showturtlehomelabelsetxy

The pendown and penup commands tell the turtle to leave ink on the screen as it moves or not leave ink, respectively. The hideturtle and showturtle commands hide or show the turtle but do not affect its ability to leave ink as it moves. The home command causes the turtle to return to the center of the screen. It may leave ink behind when it does this. These four commands do not take arguments. The label command takes a single word as a quoted string (e.g. ``a_string) or a list of words in [] brackets without quotation (e.g. [a string of letters]) and prints them on the graphics window at the location of the turtle. (Try them!) The command setxy takes two arguments, treats the first as the value of the abscissa (horizontal axis) and the second as a value of the ordinate (vertical axis). It places the turtle at these coordinates, possibly leaving ink as it does so.

What kind of figure does the following command sequence produce?

cs pu setxy -60 60 pd home rt 45 fd 85 lt 135 fd 120

Interpret these commands as you read them from left to right.

Logo Variables

A variable is the name of location that contains a value. In the random-access machine each memory location has an integer address. Since it would be hard to remember the address of each location containing a value used by a program, computer scientists

have found ways of given locations symbolic names. Once a variable has a name, we can use and manipulate it.

Variables are given names which are strings of letters, hence size could be the name of a variable. When we wish to use the value of a variable in a computation, we refer to it as :size. Note the use of the colon before the name of the variable. For example, if size has been given a value, then we can say fd :size and logo will move forward by a number of units which is the value of the variable size.

There are several ways to give a value to a variable. An explicit way to do this is described below. An implicit way will be seen when we introduce procedures. A variable can be given a value with the make command, as shown below.

make "size 60

This command gives size the value 60. Note that in this case we have used ``size, not :size. The reason is that :size is the value of the variable size, while ``size is its name. We say that ``size is the ``quoted name'' of size. Logo tries to ``evaluate'' words as it reads them because some words are the names of procedures. We quote words to tell Logo they should be not be evaluated.

The make command gives a value to a variable even if it has not yet been used in a program. In this way Logo differs markedly from Pascal. In Pascal a variable must first be given a type (``declared'') such as integer, real, or character, before it can be used. In Logo variables do not have types nor do they have to be declared before being used.

As a digression, consider the command print. It is given one argument and it prints the value of the argument in the command window. Thus, the command print 50 will print the integer 50. We introduce this command so that we can demonstrate another use of quoted names. The cleartext command, abbreviated ct, clears the text region of the command window.

Since quotation before a word means it should not be evaluated, the command print ``hello should print the word hello in the command window. Does it?

Now let's give the variable first_programmer a value which is the name of the first programmer. Try executing the following commands in the command window.

make "first_programmer "Ada_Lovelaceprint :first_programmer

Note that we quote the name of the variable first_programmer in the make command but use the colon version to obtain its value. Ada_Lovelace is quoted so it is recognized as string and not a variable. (Ada Lovelace was the first programmer.)

Arithmetic Operations

Logo provides the usual arithmetic operations of addition, subtraction, multiplication and division, denoted by the symbols +, -, *, /. Each of these operations produces a result. If you don't do something with the result, Logo will complain. With the print command the result of an arithmetic operation can be used and printed in the command window. Try the following commands:

make "size 81/9print 2*3print :size - 4

Other useful commands are sqrt, which takes one non-negative argument and returns its square root, power, which takes two arguments, call them a and b, and outputs a to the b power, denoted ab, and ln, which takes one argument and returns its natural logarithm. Other functions are exp, which takes one argument and computes e to that power, e the natural number 2.718281828, and log10, which takes the logarithm to base 10 of its one argument. For other operations, see the complete manual. Try ln 2.718281828. Whoops! Use print ln 2.718281828 instead.

Try out these ideas with the following simple code

make "angle 0repeat 1000 [fd 3 rt :angle make "angle :angle + 7]

The figure it produces is shown below.

What are the successive values of the variable angle? How many blobs does it produce? Suppose the integer 7 is changed to 11 or 13. How many blobs are produced in these cases?

Arithmetic operators have precedences that determine the order with which they are evaluated. Note that print 60 * sqrt 2 and print sqrt 2 * 60 produce different answers. Here the * operator has precedence over the sqrt operator. Thus, * will be done before sqrt if there is a choice, as there is in the second case. For this reason the first statement prints the value of 60 times the square root of 2 whereas second prints the square root of 120.

Randomization

Sometimes it is fun to have the outcome of a computation be unpredictable. Logo provides the random procedure to generate a random number. random has one

argument and produces an integer value chosen uniformly at random between 0 and the value of its argument. Thus, if you want a random angle between 1 and 360 degrees, you could use the command random 360 to produce it. Bear in mind that Logo will complain unless you do something with the result, such as print it. Try

print random 360

several times in the command window and see what it produces. For a little more fun, try

repeat 100 [fd random 80 rt 90]repeat 1000 [fd 4 rt random 360]

The first procedure produces a drawing such as that shown below. What does the second do?

Procedures

Procedures provide a way to encapsulate a collection of commands. Once a procedure has been created, it can be used just the way a built in command is used. The ``meaning'' of a procedure is the meaning of its individual commands.

A procedure without arguments has the word to (a reserved word) and the name of the procedure on the first line. (Reserved words in Logo cannot be used as variables and have a well-defined meaning and use.) It has the reserved word end on the last line. The procedure shown below encapsulates the next to the last set of instructions shown above. Aft er writing it with the editor, invoke the procedure random_walk by typing it in the command window.

to random_walkrepeat 100 [fd random 80 rt 90]end

This is dramatic evidence that a procedure merely provides a name for a set of commands.

Procedures can contain not only built in commands, they can also contain other procedures. For example, if you want to build a tree (see the figure on the next page) you will want to draw its trunk as well as its foliage. It is wise to begin experimenting with a procedure to draw a trunk. When you are satisfied with the trunk procedure, you can then construct a foliage procedure. A trunk procedure can be constructed from procedures to draw the left side of the trunk, a second to draw the top, and a third to draw the right side of the trunk. To finish up, it is prudent to have a procedure to center the turtle on the top of the trunk. From this point a circle can be drawn for the foliage. Through a series of experiments, we have constructed procedures of this kind to draw the tree shown in the figure on the next page. The procedures producing this drawing are given below.

to left_side

rt 20 fd 20 lt 20 fd 60 end

to top_side

rt 90 fd 25 rt 90

end

to right_side

fd 60 lt 20 fd 20 rt 20

end

to return_start

rt 90 fd 40

rt 90

end

to trunk

left_side

top_side

right_side

return_start

end

to center_top

pu

fd 80

rt 90

fd 20

lt 90

pd

end

to circle

repeat 360 [fd 1 rt 1]

end

to tree

pu bk 100 pd

trunk

center_top

left 90

circle

end

You are encouraged to experiment with these commands. Can you design a more realistic foliage for the tree, perhaps by modifying the circle program so that it looks a bit more ragged?

Editing Your Project

To edit your project, you will use the Xemacs editor, which starts up when you log in. You can also start Xemacs from your left mouse button. Type your procedures into your emacs window. When you are ready to try them out, select "Save Buffer" from the "Files" menu, and save your file as /u/bridgexx/src-logo/Fractal/Fractal.logo, where bridgexx is your bridge account number. Then, in your logo window, type load "Fractal.logo to load your procedures into logo's memory. When you make changes to your file in emacs, you will need to save it and re-load it into the command window.

Another, even stranger feature of the logo editor is that you cannot destroy procedures once you have created them by deleting these procedures from the editor file! Although it looks like your procedure is gone, it is still in logo's memory. To tell logo to "un-know" that procedure, you need to type erase "procedurename in the command window.

Note: Comments can be inserted on any line of a Logo program, after a semicolon. Commenting programs is highly desirable at all times. The human mind is not able to remember the details of complicated tasks and needs help. Also, without comments, a person who is not the author of a program is likely to find it much more difficult to understand and modify if the author did not properly comment it. See the fractal code below for examples.

Procedure Invocation

There is a very simple rule to explain the meaning of a procedure that invokes other procedures, including itself. It is called the copy rule. When one procedure calls another it has the same effect as if the second procedure were copied into the first.

Control

The repeat command provides control over the number of times an operation is performed. It has two arguments, the number of times to repeat a list and the list itself in brackets []. We also have the stop command which stops the execution of a procedure when it is reached. Another important control command is the if command. It takes two arguments, a ``predicate'' and a list. A predicate is an expression that evaluates to true or false. A predicate is constructed of two arguments and one of the comparison operators <, > and =. Since they are ``infix operators'' they appear between two numerical arguments, e.g. :size < 3. The following is a typical use of the if command in our abbreviated introduction to Logo.

if :size < 3 [stop]

If the value of the variable size is less than 3, the procedure stops.

Procedures with Parameters

Parameters make procedures much more useful. Following the procedure name on the first line any number of variables can be specified in the colon format, as illustrated below:

to square :sizerepeat 4 [fd :size rt 90]end

This procedure draws a square. The length of each side is size. This procedure is invoked by providing the procedure name and one parameter where the parameter is

either an integer or an integer-valued variable, e.g. square 60 or square :side where :side is an integer-valued variable.

The three procedure given below draw a crude house. The procedure house invokes the procedures square and floor.

to square :sizerepeat 4 [fd :size rt 90] ; where is the turtle when this step

completes?end

to floor :sizerepeat 2 [fd :size rt 90 fd :size * 2 rt 90]end

to housefloor 60 fd 60 floor 60 ; where is the turtle at this point?pu fd 20 rt 90 fd 20 lt 90 pdsquare 20

pu rt 90 fd 60 lt 90 pdsquare 20end

Recursive Procedures

When a procedure invokes a copy of itself, it said to be recursive. The meaning of recursive procedures is obtained in exactly the same way as regular procedural invocation, namely, via the copy rule. An example of a recursive procedure is given below. BEWARE. This procedure will run indefinitely. You will need to remember how to stop a running procedure from the command window, namely, with ^c on Unix machines (Command . on Macs).

to star to walk_the_starsrepeat 5 [fd 10 rt 144] fd 20 rt random 360end

starwalk_the_starsend

Experiment with the procedure star to see what it does. The procedure walk_the_stars moves 20 units, turns right by a random angle between 1 and 360, draws the star, and then calls itself. By the copy rule, it will repeat these operations indefinitely, that is, it never stops. It is for this reason that you must know how to stop Logo. This procedure does not tell Logo to stop.

Another illustration of recursion is given below. In this case, the procedure fractal will terminate. It is shown alongside a procedure to draw a triangle. If you look closely,

you will see that is formed from the triangle procedure by drawing a copy of a smaller version of itself along each side of the triangle. Such figures are called fractals because they have the self-similar property; they look the same at every degree of magnification. (In this case, the magnification cannot be unlimited because the figure is finite.) This particular fractal is called Serpienski's Gasket. It is very pretty.

to triangle :size to fractal :size

repeat 3 [fd :size rt 120] if :size < 3 [stop] ; the procedure stops if size is too small end repeat 3 [fd :size fractal :size/2 fd :size rt 120]end

To run fractal, type fractal 60 (or fractal x for some other integer x) in the command window.

Logo TutorialTelling Logo Where To Go

Getting Logo to move around is easy, just tell him where to go and he'll do it. Logo always looks in a special place for instructions. That place is the first line inside the main procedure. Press the Load Code button to load the code provided for you into the pane on the right side of your Logo Application window. At the top of your screen you'll see this:

procedure main end

Put the instructions you want Logo to follow below procedure main and above end.

To get started, you'll need just three simple instructions. The first instruction, go, is your way of telling Logo to walk forward in the direction he's facing. To get Logo to walk forward 50 steps, type go 50. Remember to type this inside the main procedure. Press the draw button and watch Logo walk forward 50 steps.

The other two instructions, rt and lt tell Logo which way to turn and how much. For example, to make Logo turn right 90 degrees, type rt 90. If you don't remember how degrees work, take a look at this explanation.

The Maze

Your first challenge is to get Logo out of the maze. Use the Load Maze button on your LogoApplication to draw the maze. Now use the instructions you just learned, go, rt, and lt to get Logo out of the maze. Let us know if you need help or hints.

Animation

Logo moves so fast that you really can't see him move, you can only tell where he's been by the line he draws as he moves. To slow Logo down enough that you can see him moving, we wrote a procedure, logo. It is one of the procedures that was loaded when you pressed the Load Code button. You can use logo instead ofgo to tell Logo to move slowly. To tell Logo to take 50 steps, slowly, type goto logo, steps = 50. Unfortunately, on some of your computers the screen will flicker a lot when Logo moves slowly. What can we say, animation is tricky.

Syntax

Some of you may have experienced problems by now. If you forgot to put your instructions inside the main procedure then you got an error. Also, every computer language requires you to follow very precise rules when writing instructions. These rules are known as the syntax of the language. If you do not follow these rulesprecisely Logo will not be able to underestand your instructions.

So far, you've used four Logo commands. The first three commands, go, rt and lt just tell Logo how to move. The fourth, goto, allows you to call a procedure.

Calling Procedures

The syntax for calling procedures is:

goto procedure name, parameter = value

In goto logo, steps = 50

procedure name is logo parameter is steps

value is 50.

Some procedures have no parameters, so the syntax for calling them is just:

goto procedure name

Other procedures have two parameters, and the syntax for calling them is:

goto procedure name, parameter1 = value1, parameter2 = value2

Can you figure out what the syntax for calling a procedure that has three parameters would be?

Write Your Own Procedure

You can make procedures of your own if you want. The syntax for any procedure is the same as that for the main procedure:

procedure procedure name procedure bodyend

In the main procedure you just wrote,

procedure name is main procedure body is the code you wrote to get Logo out of the maze

Do not call your procedure main; main is a special word reserved for the main procedure.

Try writing a procedure to draw a simple shape: a square or a triangle or a rectangle. This is an example of a procedure to draw a pentagon (a five-sided figure).

procedure pentagon goto logo, steps = 50 rt 360/5 goto logo, steps = 50 rt 360/5 goto logo, steps = 50 rt 360/5 goto logo, steps = 50 rt 360/5 goto logo, steps = 50 rt 360/5end

Notice that Logo can do simple math; instead of bothering to calculate 360/5 for myself, I let Logo do it.Also, I used the logo procedure because I wanted Logo to move slowly. If you want Logo to move rapidly, use the go command instead. Go ahead and call your procedure inside your main method. Use the Clear button to get rid of the maze.

Parameterize Your Procedure

The pentagon procedure is nice, but it could be better. Right now, it only makes one size of pentagon, one where Logo takes 50 steps on each side. If I make the number of steps that Logo takes a parameter of the procedure, then I can use the same procedure to draw pentagons of any size.

procedure pentagon goto logo, steps = side rt 360/5 goto logo, steps = side rt 360/5 goto logo, steps = side rt 360/5 goto logo, steps = side rt 360/5 goto logo, steps = side rt 360/5end

The new procedure uses the variable, side for the number of steps, instead of the number 50. Now, if I want Logo to draw a really small pentagon, I call pentagonlike this: goto pentagon, side = 10. If I want Logo to draw a really large pentagon, I call pentagon like this: goto pentagon, side=200. Of course, if Logo tries do draw a pentagon that big, he might walk right off the drawing space. Can you parameterize your procedure in the same way?

More Logo Instructions

Logo commands are the fundamental building blocks of the Logo language. So far, you've used just four commands, go, rt, and lt and the goto command for calling a procedure. Press the Logo Syntax button in LogoApplication to see the other commands you can use.

The repeat command is very powerful. You can use this command to call a procedure many times. These two procedures use repeat to draw a spiral. These procedures were

also loaded when you pressed the Load Code button. Try calling spiral from your main procedure. Feel free to change spiral orspiralhelper and see how that changes what Logo does.

procedure spiralhelper goto logo, steps = loop rt 50 end

procedure spiral repeat 100, spiralhelper end

Finishing Up

Do you want to save a procedure you wrote so you can use it later? To do that, open the Notepad application on your computer, copy the procedure into a Notepad document, and save it to the EYH folder on your Desktop. Name the file your_name_here.logo. We'll post your procedure on the main page so that you can access it anytime you want.