|| Logo Overnight
© 1993 Mitchel Resnick
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When most people think about Logo projects, they think of programs
that take only a few seconds (or maybe a few minutes) to run. But
this need not be the case. There are many interesting projects that
need hours of computing time. These projects are not necessarily
more complex or more difficult than standard Logo projects. They
simply take a long time to run.
Running these programs during the school day could be a problem,
since each program would monopolize a machine for hours. But there
is an easy solution: Let the programs run through the night. Students
could start running the programs when they leave school and see
the results the next morning.
Logo Overnight projects are particularly useful for exploring ideas
involving large numbers, estimation, extrapolation, probability,
and randomness. What is more, these projects can provide insights
into the scientific process. Much of experimental science involves
long-running experiments. Scientists must plan an experiment, wait
for it to run, and analyze the results. Then, based on the results,
they make changes in the experiment and run it again. Logo Overnight
projects often involve the same sort of process.
Perhaps most important, I think that Logo Overnight projects are
lots of fun. It's always exciting to go the computer the next morning
to see what has happened overnight.
Here are some ideas for Logo Overnight projects. Obviously, I hope
that students and teachers will come up with project ideas of their
own, but these examples might help them get started.
Imagine that your computer "counts sheep" at night, while you are
asleep. How many sheep would the computer count overnight?
Here's one way to investigate this question. If you use the variable
sheep to keep track of the number of sheep, then you can
write a procedure like this:
make "sheep :sheep + 1
cc show :sheep
To start the experiment, first initialize the sheep variable
(type make "sheep 0 in the command center). Then start the
Can you estimate the number of sheep the computer will count overnight?
Does it make any difference whether the computer prints out each
number as it is counting?
Monkeys at the Keyboard
If a bunch of monkeys typed randomly at computer keyboards for a
long time, what are the chances that one of them will luckily type
This Logo Overnight project will give you some sense of how likely
(or unlikely) it is for the monkeys to succeed. Instead of actually
getting a bunch of monkeys, you can write a Logo program to randomly
generate words. And it makes sense to start with an easier task:
Rather than trying to get the computer to type out all of Hamlet,
how long will it take the computer to randomly type a single word,
The program for matching "cat" could look something like this:
make "letter1 pick-letter
make "letter2 pick-letter
make "letter3 pick-letter
make "guess (word :letter1 :letter2 :letter3)
cc show :guess
make "number-of-guesses :number-of-guesses + 1
if :guess = "cat [show :number-of-guesses stop]
The pick-letter subprocedure should report a random letter from
Here's one way to write the procedure, based on the fact that the
letters a through z have "ascii values" of 97 through 122:
output char 97 + random 26
To start the experiment, first initialize the number-of-guesses
variable to 0 by typing the instruction make "number-of-guesses
0, then run the monkeys procedure.
One time, I helped a group of fourth-grade students run this experiment.
They watched as the computer printed one three-letter "word" after
another: "yhe", "rwd", "urt", and so on. We kept waiting to see
the word "cat". Suddenly, the computer printed the word "dog". All
of us had the sensation that the computer must be getting close!
If you run the experiment more than once, will you get similar
results? If you run the experiment 100 times, what is the average
number of guesses? What is the maximum? The minimum? If the computer
tries to guess a four-letter word (like "logo"), rather than a three-letter
word, how many guesses does it need (on average)? What's the longest
word that the computer can reliably guess overnight? What if you
used an alphabet with only 10 letters instead of 26 letters? What
if the alphabet had 100 letters?
If you randomly place dots on the screen, how long will it take
before the entire screen is filled with dots? You could use the
seth random 360
pu fd random 1000
pd fd 0 pu
To start the experiment, clear the screen, then run the dots
procedure. If you run the experiment several times, does it take
different amounts of time to fill the screen? It would be nice if
the program "knew" when it was finished filling the screen. How
could you do that?
What if the computer only had to fill a square, not the entire
screen? How long would it take to fill the square with dots? What
if the sides of the square were twice as long? How much more time
would it take to fill the square?
A Random Walk Down Turtle Street
Suppose that the turtle is confused about where it is going. With
each step, it is equally likely to take one step forward or one
step back. How quickly will the turtle get anywhere?
Let's say you start the turtle at the middle of the screen. Where
do you think the turtle will be by the next morning? What is the
furthest that the turtle will have wandered from "home" during the
night? If the turtle steps were twice as large (or half as large),
how would the answers be different?
You could use a procedure like this:
ifelse (random 2) = 0 [fd 1][bk 1]
if ycor > :ymax [make "ymax ycor]
if ycor < :ymin [make "ymin ycor]
The variables ymax and ymin keep track of how far
"up" and "down" the turtle has wandered. You should initialize each
with a value of 0 by typing the instructions make "ymax 0
and make "ymin 0.
Actually, there is a bug in this procedure, since the turtle could
"wrap" around the screen during its walk. How can you fix this bug?
When's Your Birthday?
If you are in a room with 30 people, what are the chances that two
of the people have the same birthday? Are the chances better than
Here's one way to investigate this question. Start the Logo turtle
in the middle of the screen, heading at 45 degrees. Pick a number
between 0 and 364 (representing a day of the year), move the turtle
forward twice that distance, and make a dot. That dot represents
one person's birthday. Then repeat the process, making dots for
the other 29 birthdays. If the turtle ever puts two dots on the
same spot, then two of the birthdays match. (Note: the turtle moves
forward twice the random number, to make sure that nearby
dots, representing nearby dates, do not "overlap" by accident.)
Here's a Logo procedure implementing this strategy. (The procedure
assumes that the variable people has been initialized to
0. You may do this with the instruction make "people 0.)
make "people :people + 1
if :people > 30 [output "false]
pu home seth 45
fd 2 * random 365
if colorunder = 1 [output "true]
pd fd 0 pu
What if you run this experiment many times? It's as if you keep
entering new rooms, each with 30 people. What fraction of the rooms
will have "birthday matches"? The birthday procedure runs the experiment
over and over, keeping track of the number of matches:
make "experiments :experiments + 1
if any-matches? [make "matches :matches + 1]
make "people 0
To start the investigation, initialize experiments and matches
to 0, then run the birthday procedure. After a long time,
what is the value of matches divided by experiments?
Do more than half of the experiments result in matches? What if
there were 25 people in each room? What if there were 40 people
in each room? What if there were 367 people in each room?
These examples are intended to give you some ideas, to help you
get started with Logo Overnight. The real challenge is to think
of your own Logo Overnight projects.
It's a waste to let your computers sit idle at night. So start
putting them to work!
Appendix - Different Versions of Logo
The projects described in this paper may be carried out in almost
any version of Logo. However, the programs were developed using
the MSDOS version of LogoWriter and may not work exactly as written
in other versions of Logo, or even the Macintosh or Apple IIe versions
of LogoWriter. Although the required changes are minor, they may
Here are some ways in which you might need to modify the programs
in order for them to work in your version of Logo:
- You cannot use procedure names like count-sheep or variable
names like number-of-guesses in most versions of Logo because
of the - character.
- The command cc to clear the command center is used only
in LogoWriter. In other versions you might need cleartext,
- The syntax of if and ifelse varies from version
- The procedure make-a-dot may not work as written. In
some versions of Logo, fd 0 does not leave a dot. You could
use fd 1. Your version may have a dot procedure.
To put a dot at the turtle position you may need to use the instruction
dot pos or dot xcor ycor, depending upon your version.
- Instead of rg (reset graphics) to clear graphics from
the screen, you may need to use clearscreen, cs,
- Colorunder is not available in all versions of Logo.
Alternatively, you may be able to use dotp or dot?
to detect a dot on the screen.