A LogoWriter Ecology Simulation by Thomas F. Trocco
	© 1989 LCSI © 1993 Thomas F. Trocco Computer & Science Department Chair Computer Teacher, Grades 2 - 8 St. Hilda's & St. Hugh's School New York, NY

Presented at the April 13, 1993 New York Logo Users Group meeting.

Acknowledgements

Thanks to Michael Tempel, Steve Neiman, Andrew Newcomb, Eliot Widaen, and Diane Linder for their interest, suggestions, editing, and discussion. Special thanks to Michael and Diane for their suggestions on mating proximity; to Eliot for the birth placement concept; to Andy for his editing suggestions; and to Steve for his help with Apple IIGS compatibility. Extra-special thanks to Tyler Barnes, Tracy Blount, Vanessa Cook, Matthew Graves, Maritza Schaeffer, Austin Shau, and Laura Stickney for their presentation at the Logo Users Group.

You may copy and distribute this document for educational purposes provided that you do not charge for such copies and that this copyright notice is reproduced in full.

Correspondence can be sent to:
Thomas F. Trocco
The Calhoun School
433 West End Avenue
New York, NY 10024

Introduction

With the release of an ever-increasing number of simulation programs (e.g., Sim Ant, Sim Earth, etc.), students have much more to work with than just the original Lemonade Stand program of ten years ago. However, creating a simulation from scratch can teach students much more than using off-the-shelf software.

Computers are excellent tools with which to simulate real events: variables can be controlled and altered at will and events can occur faster than in real time. After trying various simulation programs, I found myself wondering how my sixth grade students and I might create such a program with LogoWriter. Our sixth grade class spent a week in the New England countryside with Nature's Classroom in the fall, and came back to school with some knowledge of predator-prey interactions. They continued their studies in science class. When I suggested to the students that they try to create their own predator-prey simulations in LogoWriter, they jumped at the chance.

LogoWriter, with four turtles and the ease with which it allows animation to be coded, is an excellent workbench for creating simulations. Before my students began work on their own simulations, I programmed a more complex version. This fulfilled two purposes. First, working on a complex Logo problem gives me great enjoyment. Second, whenever I assign a long-term complex task to my students, I try produce a simple version first so I can anticipate problems and guide them when necessary. In this case, I enjoyed the task so much that I created a much more complex version than usual.

With student projects, I usually strive to have the entire class have the same underlying program structure. Upon this foundation each student can add his/her own modifications. Throughout the project, I have stressed that the worlds the students created are their own, and may follow any rules, as long as a consistent logic holds true. Most solutions have come from the students, though at times I have given hints and prodded them towards a specific solution when too much time passed without a workable answer to a problem. The duration of this unit was one semester, with one or two class meetings per week.

The Setting

Students at St. Hilda's and St. Hugh's School practice keyboarding and use educational software in Nursery through first grade with their classroom teachers. Beginning in second grade, children also work with LogoWriter in the computer lab. The students meet with me once or twice a week for programming projects. Each class is forty minutes long. Class size varied this year from nine to twenty students. I usually begin each unit by introducing a new command or concept, or by posing a question or problem. Then the students work on experimentation, application, and testing throughout the duration of the unit, which can vary from one period to as long as one semester. Often, there are a few interrelated concepts and questions being worked on simultaneously. Units this year included word processing and book-making in the second grade, animated sentences in the third grade, coordinate plotting of designs in the fourth grade, ancient Egypt-based projects in the fifth grade, derivation of Pi and the creation of pie graphs in the sixth grade, and independent programming projects (branching stories, animation, music 'videos', and multiple choice Latin exams) in the seventh and eighth grades. Many classes also use the lab for Writer's Workshops using LogoWriter or Word Perfect with their language arts teachers. The lab currently contains twenty-one MS/DOS computers (ranging from monochrome XTs with no hard drives to PS/2s) running LogoWriter 2.0.

Development of My Simulation

To lay a foundation for this project, I decided on the parameters for my ecosystem. My ecosystem would:

• be aquatic
  
• have one species of plant
  
• have one species of herbivorous fish
  
• have one species of carnivorous fish
  
• have two adults, male and female, of each fish species
  
• have the herbivores eat only plants
  
• have the carnivores eat only the herbivores
  
• have fish mate only with members of the same species
  
• have a random number and random distribution of plants each time the simulation was run

The number of species and the number of individuals per species were chosen for simplicity and because of LogoWriter's limitation of four turtles. I chose an aquatic ecosystem so my scenery would be simple: with no horizon line, the entire screen could use one background color.(see Figure 1 for a screen print-out) I next began creating the shapes needed for the ecosystem.(shape 2 was later removed) Shape numbers 1 through 8 were used (see Table 1 and Figures 2 - 8). Even-numbered turtles (0 & 2) were used for the herbivores and odd-numbered turtles (1 & 3) were used for the carnivores.(see Table 2) I began programming this project on a four-color CGA IBM/PC, so I decided to begin with three screen colors for my three species. I chose white for herbivores, cyan for plants, and magenta for carnivores. Other colors were added later for other platforms.(see Table 3a)
I began with a setup procedure to clear the screen:

to setup
rg
end

I then wrote a set.fish procedure to give the four turtles their proper shapes, colors, and headings:

to set.fish
tell all st pu home
tell 0 setsh 3
tell 1 setsh 6
tell 2 setsh 4
tell 3 setsh 7
tell [0 2] setc 1 seth 90
tell [1 3] setc 3 seth 270
end

The heading depended on whether the fish was facing left (seth 270) or facing right (seth 90).

However, before the fish begin to move, the plants should be stamped on the screen.

to set.grass
setsh 1 setc 2
end

to grow.grass
repeat 25 + random 25 [plant.grass]
end

to plant.grass
pu
setpos list random 320 ((-1 * random 94) + 8)
pd
stamp
end

Set.grass sets the shape and color of the turtle. Grow.grass calls the plant.grass procedure between 25 and 49 times, randomly. Random was used to give the simulation some variation each time it ran. The range was chosen to have sufficient plants for feeding, but not so many that the screen was mostly stamped plants. The plant.grass procedure places the turtle at a random position and stamps it. Setpos requires a list of two numbers as input. Random 320 was chosen as the first, or "x" value, because this is the width of an IBM screen. For the "y" value, I wanted plants only in the lower half of the screen. Since the IBM screen is 189 pixels high, I chose one-half of that, or 94. By multiplying this by -1, only points in the lower half of the screen will be addressed. However, since shapes are 16 pixels high (in IBM, Apple IIGS, C64), I added half of this, or 8, to the number so the plants wouldn't be split between the bottom and top of the screen.

I was now ready to animate my fish with a begin procedure, using herb and carn:

to herb
fd random 10
end

to carn
fd random 10
end

to begin
tell 0 herb
tell 1 carn
tell 2 herb
tell 3 carn
begin
end

The begin procedure caused the four turtles to move across the screen one at a time anywhere from 0 to 9 steps each time by using forward with a random 10. Begin then calls itself, and continues until a stop command is entered from the keyboard.

Because the headings had been set at either 90deg. or 270deg., the fish would only move horizontally. Just as I had used random for fd, I could also use it for heading. I modified the herb and carn procedures:

to herb
fd random 10 seth 248 + random 45
end

to carn
fd random 10 seth 68 + random 45
end

Because of the way I had designed the shapes, the carnivores had to face right, and the herbivores left. By using random, the heading could vary but still face in the correct general direction. I chose a range of 44 degrees by using random 45 which reports a range of 0 to 44. To face right, 68 + random 45 was used. This reports a range of 68 to 112, with an average of 90. To face left, 248 + random 45 was used. This reports a range of 248 to 292, with an average of 270.
With this enhancement, herbivores and carnivores moved around the screen with random distances and headings, colliding with each other randomly with a satisfactory frequency. I now needed to program feeding and mating.

to herb
fd random 10
seth 248 + random 45
if equal? colorunder 2 [feed]
if equal? colorunder 1 [herb.mate]
end

to carn
fd random 10
seth 68 + random 45
if equal? colorunder 1 [feed]
if equal? colorunder 3 [carn.mate]
end

Now, as the animals moved around the screen, the program tested for colorunder. Whenever a carnivore passed over color 1 (an herbivore), feed would be called, and whenever it passed over color 3 (the other carnivore), carn.mate would be called. For an herbivore, feed would be called whenever it passed over color 2 (a plant), and herb.mate would be called whenever it passed over color 1 (the other herbivore).

Feed was simple to program:

to feed
pe fill pu
end

Feed erases as much of the food shape as can be filled in, depending on the location and "contiguousness" of the pixels.

The two mating procedures work by first setting the shape of the female to the baby's shape, stamping this shape to the screen, then setting the shape back to the mother's. The fd 20 commands, which produce a "rebound" effect, were added because multiple matings were occurring as adults of the same species remained in close proximity.

to herb.mate
tell 2 setsh 5
pd stamp pu
setsh 4 fd 20
end

to carn.mate
tell 3 setsh 8
pd stamp pu
setsh 7 fd 20
end

Some problems arose at this point. While herbivores could feed on plants by erasing them, a carnivore feeding on an adult had no effect on it because a turtle cannot be erased. In addition, once babies began to be stamped on the screen, adults would mate as they passed over their offspring. I also discovered at this point that in Macintosh and Commodore 64 LogoWriter, while colorunder will test for colors stamped, filled, or drawn on the screen, it will not test for turtle color. Another test had to be used. One solution is to test for the distance between the male and female.(See the end of the program listing for an example.) The program at this point was as follows:

to startup
setup
set.grass
grow.grass
set.fish
begin
end

I had successfully written a simple simulation. I was really quite excited seeing my fish move around the screen, feeding and stamping babies! While this was a good start, I wanted to go further. I drew up a list of features I wanted. Many of these were arbitrary, but I decided that I could create any rules for my ecosystem as long as there was a consistent logic applied:

• The simulation should not be tied to any one platform running LogoWriter
  
• The number of feedings should be tallied
  
• The number of births should be tallied
  
• The two species should give birth in different areas of the screen to reinforce their niche differences
  
• A timer should be added, so feeding and mating rates could be calculated and compared
  
• Grass should continue to grow throughout the simulation
  
• Fish should not wrap around the screen vertically because it looks odd
  
• Adult and offspring should be different colors to avoid intergenerational mating
  
• Carnivores should eat herbivore babies, but not herbivore adults
  
• Carnivores should eat their own offspring some of the time (life is tough)
  
• Females should be able to reproduce parthenogenically after having fed a specified number of times
  
• Proximity, and not COLORUNDER, must be used for mating to allow for Macintosh and C64 compatibility
  
• Species-specific courtship rituals should be added
  

These features were added to the simulation.(See annotated program listing in Addendum A. A flow chart is shown in Figure 9)
While this simulation can now run on all versions of LogoWriter, be aware that it will be quite slow when running on anything slower than an IBM 286. For Apple IIGS LogoEnsemble users, type newpage40 to set 40 columns before you name your page. Because the Commodore 64 has very little available memory and because only LogoWriter 1.1 is available for it, many deletions and modifications have to made.(See Addendum D)

Development of a Student Simulation

To lay a foundation for the student project, I asked each student to come up with a set of rules for ecosystems in general. They merged these into a combined list, then derived a shorter list of general rules from these during a brainstorming session. The next step was to divide students into cooperative groups of four or five students each. Each group had to decide what type of ecosystem they wanted, and to state rules for their ecosystem. I created 3 groups of four boys and one group of five girls.

For simplicity, each ecosystem was allowed only one predator species, one prey species, and one plant species. Students then began creating the shapes needed for their ecosystem.(See Table 1 and Figures 1-8.) For class-wide consistency and easier teacher debugging, I suggested using even-numbered turtles (0 & 2) for the herbivores, odd-numbered turtles (1 & 3) for the carnivores (See Table 2) white for herbivores, cyan for plants, and magenta for carnivores. Other colors, if available, were used for scenery and background.(See Table 3b) We began with a setup procedure to give the four turtles their proper shapes, colors, and headings:

to setup
tell all st pu home
tell [0 2] setc 1 seth 90
tell [1 3] setc 3 seth 270
tell 0 setsh 3
tell 1 setsh 6
tell 2 setsh 4
tell 3 setsh 7
end

The heading depended on whether the animal was facing left (seth 270) or facing right (seth 90).

The next step was to create scenery for the ecosystem. Students wrote procedures to stamp their plants on the screen. For terrestrial ecosystems, students split the screen with a horizon line. Other components, such as ponds, mountains, etc., were added by some students. A typical scenery procedure is shown below: (See Addendum F for full program listing)

to scenery
scene
pond
trees
sun
end

Students then spent a few weeks creating scenarios, such as a giraffe walking up to a tree and eating from its crown, or a wolf chasing a deer. The girls initially concentrated on mating and giving birth, whereas the boys had concentrated on predation. With reporters from each group often seeing what others were doing, the girls added predation and the boys added mating. My reason for creating an all-girl group had been to allow for full female expression. This was successful and had affected the boys as I had hoped. After all groups completed this stage, the students watched each other's simulations. They realized that they had created plays with actors following set lines, rather than free-flowing and unpredictable simulations. I suggested that it might be possible to move the animals around the screen randomly so that interactions could not be predicted. We wrote a move procedure, using herb and carn:

to herb
fd random 10
end

to carn
fd random 10
end

to move
tell 0 herb
tell 1 carn
tell 2 herb
tell 3 carn
move
end

The move procedure caused the four turtles to move across the screen anywhere from 0 to 9 steps each time by using forward with a random 10.

Next, students wanted to be able to have their animals eat, so I introduced colorunder. They modified the herb and carn procedures as follows:

to herb
fd random 10
if equal? colorunder 2 [eat]
end

to carn
fd random 10
if equal? colorunder 1 [eat]
end

As in my program, as the animals moved around the screen, the program tested for colorunder. If the carnivore passed over color 1 (an herbivore), it would eat, while an herbivore would eat whenever it passed over color 2 (a plant). It was now up to the students to devise an eat procedure. In a class discussion, three possibilities were suggested:

to eat This takes a chunk out of the food the size and shape of
pe stamp pu the eater. One student likened it to a cartoon where a
end character runs through a wall and leaves a hole its size
and shape.

to eat This erases as much of the food shape as can be filled in
pe fill pu depending on the location and contiguousness of the
end pixels.

to eat
pe fd 1 pu This takes a one-pixel bite out of the food.
end

Students decided which of these three they wanted to use. Most chose to use fill. They realized that when the carnivore passes over an herbivore, it won't affect it because while a stamped shape can be erased, a turtle cannot. Students then decided to have their animals give birth so that stamped babies could be eaten. To tackle the programming to control mating, colorunder was used again. Since the students were working in MSDOS LogoWriter, colorunder does test for turtle color. This was added to herb and carn:

to herb
fd random 10
if equal? colorunder 2 [eat]
if equal? colorunder 1 [h.mate]
end

to carn
fd random 10
if equal? colorunder 1 [eat]
if equal? colorunder 3 [c.mate]
end

Now, if one carnivore passed over another, it would call the c.mate procedure. Likewise, if one herbivore passed over another, it would call the h.mate procedure.

to h.mate
tell 2 setsh 5
pd stamp pu
setsh 4 fd 20
end

to c.mate
tell 3 setsh 8
pd stamp pu
setsh 7 fd 20
end

These procedures work by first setting the shape of the female to the baby's shape, stamping this shape to the screen, then setting the shape back to the mother's. Students added the fd 20 commands, to avoid the multiple matings that occurred as adults of the same species remained in close proximity.

In some cases, no matings occurred because males and females of the same species would never collide during a simulation run. Students saw that if animals were at different places vertically on the screen and only moved horizontally, they would never meet. Some students then realized that just as they had used random for fd, they could also use it for heading. Again, they modified the herb and carn procedures:

to carn
fd random 10
seth 248 + random 45
if equal? colorunder 1 [eat]
if equal? colorunder 3 [c.mate]
end

to herb
fd random 10
seth 68 + random 45
if equal? colorunder 2 [eat]
if equal? colorunder 1 [h.mate]
end

Students decided that the heading should vary by a small range, because when larger values were used, the animal appeared to be jumping around the screen. Most students chose my suggested "window" of 45 degrees.

Students did not like to see their animals wrapping around the screen top and bottom, so two final lines were added to both herb and carn:

if ycor > 0 [descend]
if ycor < -80 [ ascend]

The minimum and maximum values for ycor, the "y" coordinate, or vertical location, depend on what part of the screen a student wanted to allow the animals to roam in. These values varied for each group.

Descend and ascend simply moved the turtle in question up or down:

to descend
seth 180
repeat 20 [fd 1]
end

to ascend
seth 0
repeat 20 [fd 1]
end

Personal Successes

• I found myself forced to tackle some concepts which I had previously avoided. Naming variables by using word and the number of the turtle in question:

  make word "eatcnt who 1 + thing word "eatcnt who

  allowed me to write shorter code which was then applicable to all four turtles, rather than writing four separate procedures.

• The frustrations of creating a procedure that would run under eight different platforms (IBM- CGA, IBM-EGA, IBM-VGA, Apple II, Apple IIGS, LogoEnsemble, Commodore 64, and Macintosh) forced me to use variables for screen sizes and colors in ways I never would have otherwise.

• The problem of colorunder not working on the Macintosh the same way as in other platforms forced me to work out the Pythagorean Theorem in LogoWriter (with twenty parentheses!)

• The problem of colorunder not working on the Commodore 64 the same way as in other platforms coupled with a lack of the sqrt function forced me to work out a different distance test, based on absolute value, in LogoWriter.

• As I was working on this for my own enjoyment, my sixth graders were working on similar simulations. I was able to anticipate some problems, and guide them more efficiently.
  

Successes in the Classroom

This project was largely student-designed and directed, and created more interest than almost any other project and class I've worked with. New concepts, such as colorunder and random, were introduced as they were needed. Student understanding and application of these concepts was rapid and flexible. Previously learned concepts, such as third grade animation, heading, multiple turtles, and turtle interactions have been reinforced and expanded upon. Students were able to work in groups, individually, and as a class during this project. Science and classroom teachers stopped by to see our progress.

Problems with Program Execution

• With CGA graphics on the IBM PC, only three pencolors are possible. Because of this, animals "mate" with their offspring, and feeding is counted when carnivores pass over herbivores, even though they have no effect on their prey. On any other platform, at least 5 colors would be available, and offspring could be stamped a different color than their parents.

• LogoWriter is slow to begin with. This simulation, with up to seven levels of sub-procedures, runs slowly even on a fast IBM. I have used Apple File Exchange to pull this simulation as a text file into the Macintosh, the Apple IIe, and the Apple IIGS where I could tinker with it. On Apples and on slower Macintoshes, it is very slow. There is no loadtext command for Commodore 64 LogoWriter 1.1, so I had to retype it. Because of memory limitations, extensive modifications had to made for it to run on the C64.(See Addendum D) Even then, it is painfully slow at 1 MHz.
  

Problems in the Classroom

As with any semester-long project, it is sometimes difficult to maintain a high level of student interest. The main obstacle for most students was the limitation of three pencolors with CGA graphics. Some students found parent-offspring matings disturbing. I challenged the students to devise solutions to this problem. Laura, who was working with 16-color EGA, chose to use different colors for the offspring. Austin stamped his babies on the bottom of screen where the parents didn't go. I did not have time to introduce a distance test, rather than colorunder, and no student thought of it during our project.

Proposed Experimentation and Additions:
Using the Simulation as a Science/Math Lab Resource

This simulation can now be run a number of times to see the outcomes. Values of variables can be changed to see how that affects the outcome.

Some questions I have not yet investigated are:

• What happens if predator and prey move at greatly different speeds?
  
• Is there a way to measure population growth and overpopulation?
  
• Could animals be made to die as their food source disappears?
  
• Could waste or pollutants be made to build up during a simulation run? (addressed by one student, Austin)
  
• Could a species be made extinct if the ratio of feeding to time becomes unfavorable?
  
• Could disease or parasite infestation be made to increase as population size increases?
  

Those students who are interested will now have time to implement some of their suggestions.

Some questions I have looked into are:

• Within one simulation run:
  • Do males and females of the same species behave differently?
    Do carnivores and herbivores mate at the same rate?
    Could statistics such as the number of feedings and matings be kept as the
    program runs?
    
• Comparing different simulation runs:
  • Will the number of matings or feedings differ greatly each time the program is run?
    What is the distribution pattern of the feeding or mating frequencies?

To collect data on these questions, I added a stats (statistics) procedure to my simulation:
to stats
ef
if member? "stats filelist [loadtext "stats] bottom
(pr :day :eatcnt0 :eatcnt2 :eatcnt1 :eatcnt3
:h.births int :eatcnt2 / 20
:c.births int :eatcnt3 / 20)
if member? "stats filelist [erasefile "stats]
savetext "stats
end

Stats first clears the text screen. If there is already a stats file on the disk, it is loaded. The cursor is moved to the bottom of the text screen. The values of the following variable are printed on the screen:

This procedure was then added to rollover, so it would be called once a day at 12 midnight:

to rollover
stats
make "time 0
make "meridian "AM make "day :day + 1
end

The simulation was allowed to run overnight, until 521 simulated days' worth of data had been accumulated. These data were then graphed with PFS First Graphics. The male and female carnivore feeding rates stay approximately equal during the 521 day run.(See Figure 10) Females end up slightly higher at the end of the run. Male and female herbivore feeding rate stay equal until day 150, after which the male rate decreases. Since the movements around the screen are random, this raises interesting questions. Could the female rates be higher because they spend more time near the top (carnivore) or bottom (herbivore) of the screen, thus avoiding male competition? Or is it because the turtles are moving at the rate of who + fd 5, and the females, with their higher turtle numbers, move faster than the males? By making the fds all the same, this question could be answered.

Herbivore and carnivore births were compared. (See Figure 11) Here, equal rates were expected for births dues to matings (from random collisions), but higher parthenogenic rates were expected for herbivores, since they feed much more often than carnivores. Surprisingly, the carnivore birth rate (1391 births/521 days, or approximately 2 2/3 births/day) was much higher than the herbivore birth rate (873 births/521 days, or approximately 1 2/3 births/day). I am at a loss to explain these differences.

In addition to analyzing summed data, numerous daily data can be collected and compared. I changed rollover to:

to rollover
stats
clearnames
start
end

This will allow the simulation to run for only one day before all variable values are cleared and the program starts again. I let it run for 112 daily cycles.

I then divided the feedings per day into groups of ten for the herbivores and groups of three for the carnivores so I could graph the data discretely on a histogram rather than continuously with a line graph. I counted the feeding frequencies for males and females of both species. For example, there were 0 days when the herbivore females fed 0-10 times, 5 days when they fed 11- 20 times, 20 days when they fed 41-50 times, etc. (See Figure 12 for herbivores, Figure 13 for carnivores) All four approach normal distributions. Possibly with a larger sample, a smoother normal distribution could be seen.

This type of data collection and analysis could be an excellent way to introduce students to normal distribution, to statistics, and to use of the computer as a math/science laboratory.

Addendum A

to start
setup
set.grass
grow.grass
set.fish
begin
end

to ef
if not front? [flip]
ct
end

Ct (cleartext) is dangerous to use because if it is used in the command center of your flip side, ALL text (i.e., all procedures) will be erased. I urge you to put this EraseFront procedure on each of your pages, and use ef instead of ct. This procedure will clear the text only after you have flipped to the front side.

to setup
rg
ht
ef
cc
make "width 320
make "height 190
make "eatcnt0 0
make "eatcnt1 0
make "eatcnt2 0
make "eatcnt3 0
make "day 1
make "time 0
make "meridian "AM
make "herb.m.s 3
make "herb.f.s 4
make "herb.b.s 5
make "carn.m.s 6
make "carn.f.s 7
make "carn.b.s 8
make "plant.sh 1
make "h.births 0
make "c.births 0
make "male "M
make "female "F See Addenda B - E for additions or deletions here.
setbg :water.5 Keep this as the last line in this procedure even as end other lines are added.

The setup procedure creates a number of global variables used throughout this program:

:width :height :eatcnt0-3 :day :time :meridian :herb.m.s :herb.f.s :herb.b.s :carn.m.s :carn.f.s :carn.b.s :plant.sh :h.births :c.births :male :female

is the width of the screen in pixels. is the height of the screen in pixels. will keep a count of how many times turtles 0-3 have eaten. is first set to 1. is first set to 0. is first set to AM. is the herbivore male shape number. is the herbivore female shape number. is the herbivore baby shape number. is the carnivore male shape number. is the carnivore female shape number. is the carnivore baby shape number. is the plant shape number. will keep a count of herbivore births. will keep a count of carnivore births. is set equal to the letter M. is set equal to the letter F.

Modifications to Setup for Different Platforms

Most of these lines set the colors of the fish, plants, and water.(See Table 3a) Other lines are explained in the addenda.(IBM users see Addendum B. Apple users see Addendum C. Commodore 64 users see Addendum D. Macintosh users see Addendum E.)

to set.grass
setsh :plant.sh
setc :plant.color
end

Sets the turtle to the plant's shape and color.

to grow.grass
repeat 25 + random 25 [plant.grass]
end

to plant.grass
pu setpos list
random :width ((-1 * random (:height / 2)) + 8)
pd stamp
end

Sets the position of the turtle anywhere along the width of the screen, and anywhere in the bottom half of the screen.

to set.fish
tell all st
pu home
tell 0 setsh :herb.m.s
tell 1 setsh :carn.m.s
tell 2 setsh :herb.f.s
tell 3 setsh :carn.f.s
tell [0 2] setc :herb.color
tell [1 3] setc :carn.color
end

Sets the four turtles to their proper shapes and colors.

to begin
tell 0 herb
tell 1 carn
tell 2 herb
tell 3 carn
circadian
begin
end

Moves each turtle alternately, updates the timer (see circadian), then calls itself recursively.

to herb
seth 248 + random 45
fd who + random 5
if equal? colorunder :plant.color [feed eat.count]
ask 0 [make "pos0 pos]
ask 2 [make "pos2 pos]
if ((hypotenuse :pos0 :pos2) < 16) [herb.mate give.birth]
swim.test
end

The heading is set to the left, anywhere from 248 to 292. The turtle moves forward a number of steps equal to random 5 plus its turtle number. Who was added to the random so that males and females would move at different speeds. If the colorunder is equal to the plant color, feed is called, then eat.count (see eat.count). The positions of the male and female are stored in variables and these values are passed to hypotenuse. If the distance between the two turtles is less than 16 steps, herb.mate and give.birth are called. This distance can be changed to a different value depending on how "attracted" you want your males and females to be to each other. See swim.test below.

to carn
seth 68 + random 45
fd who + random 5
if equal? colorunder :herb.baby [feed eat.count]
if and (equal? colorunder :carn.baby)
(equal? 0 (random 2)) [feed eat.count]
ask 1 [make "pos1 pos]
ask 3 [make "pos3 pos]
if ((hypotenuse :pos1 :pos3) < 16) [carn.mate give.birth]
swim.test
end

This procedure is identical to herb with the following exceptions:

• The heading is set to the right, from 68 to 112.
  
• If the colorunder is equal to the herbivore baby color, feed is called, then eat.count (see eat.count).
  
• If the colorunder is equal to the carnivore baby color, feed and eat.count are called randomly about 50% of the time (see eat.count).
  
• Position is used identically, but with different variable names. See swim.test.
  

to swim.test
if ycor > :height / 2 - 24 [seth 180 swim]
if ycor < 8 - :height / 2 [seth 0 swim]
end

If the turtle is within 24 steps of the top of the screen, the heading is changed to 180 and swim is called. If the turtle is within 8 steps of the bottom of the screen, the heading is changed to 0 and swim is called. This keeps the turtle from wrapping around the screen top and bottom.

to swim
repeat :height / 2 [fd 1]
end

The turtle moves away from where it is a distance of half the height of the screen.

to eat.count
cc
make word "eatcnt who 1 + thing word "eatcnt who
if member? who [2 3] [check.feedings] type [The number of feedings is:]
t13
(type :male [herb=] :eatcnt0 [;] :female [herb =] :eatcnt2)
t13
(type :male [carn=] :eatcnt1 [;] :female [carn =] :eatcnt3)
t13
(type [herb births =] :h.births [; carn. births =] :c.births)
end

This procedure tallies feedings and displays the current values.

make word "eatcnt who 1 + thing word "eatcnt who

This works by adding 1 to the current value (thing) of the variable called :eatcnt0, :eatcnt1, :eatcnt2, or :eatcnt3. Which eatcnt variable is used is determined by making a word out of eacnt plus who, the number of the turtle which called this procedure. If the turtle in question is female [2 3], check.feedings is called.

The current values of the numbers of feedings for each turtle and the number of matings for each species are displayed in the command center.

to check.feedings
if equal? 0
(remainder thing word "eatcnt who 20)
[make word "eatcnt who 1 + thing word "eatcnt who labor]
end

Females will give birth parthenogenically every twenty times they feed. If the number of times they have fed divided by 20 gives a remainder of zero, labor is called.

to labor
ifelse equal? who 2 [seth 180 descend] [seth 0 ascend]
give.birth
end

If the turtle in question is 2, it will face down and descend, otherwise, it is turtle 3 and it will face up and ascend. give.birth is called.

to t13
type char 13
end

Moves the cursor to the next line in the command center.

to feed
pe fill pu
end

Feeding is accomplished by erasing what is under the turtle's pen. This can vary from one pixel to a large area, if the color is contiguous.

to give.birth
birth.check
ifelse equal? who 2
[setsh :herb.b.s setc :herb.baby pd stamp pu setsh :herb.f.s setc :herb.color seth 270][setsh :carn.b.s setc :carn.baby pd stamp pu setsh :carn.f.s setc :carn.color seth 90]
swim
end

See birth.check.

If the turtle is #2, the herbivore baby color and shape are set, and stamped. Otherwise, the carnivore baby color and shape are set and stamped. The shape and color of the female is restored. See swim above.

to birth.check
if member? colorunder
[:herb.baby :carn.baby]
[fd 9 birth.check]
end

If the colorunder the female is already that of her own baby, she will move 9 steps. This continues until a clear birthing area is found.

to circadian
ef
make "time :time + 1 make "hour (int :time / 60)
make "min remainder :time 60 if equal? :min 0 [water]
if :min < 10 [make "min word "0 :min]
make "display word (word :hour ":) :min
if equal? 0 (remainder :time 1440) [rollover]
(insert [It is day] word :day ", :display :meridian)
if equal? (random 50) (0) [random.grass]
end

This is a completely arbitrary timer. Possibly those with Macintoshes may want to use the clock built into the computer. Time is incremented by 1. The hour is equal to the integer value of :time divided by 60. The minutes are equal to the remainder of :time divided by 60. If :min are equal to zero (i.e., every hour on the hour), the water procedure is called. If :min is less than 10, a zero is added in front to pad the number. Whenever :time is equal to a multiple of 1440, rollover is called. The day and time are displayed. Approximately 1 out of 50 times (2%) one grass will be stamped with random.grass.

to water
if equal? :hour 6
[setbg :water.1] if AND :hour > 6 :hour < 12
[setbg :water.2] if equal? :hour 12
[setbg :water.3 make "meridian "NOON]
if :hour > 12
[make "meridian "PM]
if equal? :hour 18
[setbg :water.4] if :hour > 18
[setbg :water.5]
end

The background color is changed at 6 am, 12 noon, 1 pm, 6 pm, and 7 pm (for the APPLE II, with its 6 colors, all values of :water.? are black).

to random.grass
make "pos pos
make "shape shape
make "color color
set.grass
plant.grass
setsh :shape
setc :color
pu
setpos :pos
end

This procedure will randomly plant grass on the screen. Because all four turtles are already being used for the four fish, the computer must first store the position, shape, and color of the turtle in question. After one grass has been stamped, the position, shape, and color are restored. This happens so fast that only a momentary blinking is seen.

to rollover
make "time 0
make "meridian "AM
make "day :day + 1
end

This will reset the time to 0, and increment the day by 1.

to herb.mate
tell [0 2] repeat 12 [fd 2 rt 30]
repeat 12 [fd 2 lt 30]
tell 2 seth 180
descend
make "h.births :h.births + 1
end

to carn.mate
tell [1 3]
seth 45
repeat 8 [fd 5 rt 90 fd 5 lt 90]
repeat 8 [bk 5 rt 90 bk 5 lt 90]
tell 3 seth 0
ascend
make "c.births :c.births + 1
end

These two procedures are the different courtship dances performed by these two species. The number of births is incremented by 1.

to descend
fd 1
if ycor < 10 + (random 10) - :height / 2 [stop]
descend
end

The turtle will keep moving until it is within 10 to 19 steps of the bottom of the screen.

to ascend
fd 1
if ycor > :height / 2 - 24 - random 24 [stop]
ascend
end

The turtle will keep moving until it is within 24 to 47 steps of the top of the screen.

to hypotenuse :a :b
op (sqrt ((sq ((first :a) - (first :b))) + (sq ((last :a) - (last :b)))))
end

The inputs to hypotenuse are the position of the two turtles in question. Position is a list of two numbers (xcor and ycor). Hypotenuse will report the straight line distance between the two turtles by using the Pythagorean Theorem. The first of a position in its xcor, and the last is its ycor. The squared differences in the xcors are added to the squared differences of the ycors, and the square root of this sum is output.

to sq :num
op :num * :num
end

Outputs the square of a number. Used in hypotenuse.

Or

I needed an alternative for the Commodore 64, which does not have sqrt in its LogoWriter 1.1. It was also suggested to me that a simpler measure of distance be used so that younger students will understand the procedure (summing the difference in Xs and Ys - a measure known as Manhattan Grid Distance). My solution was to sum the absolute values of the difference in "x" values and the difference in "y" values. This will work for any version of LogoWriter.

to hypotenuse :a :b
op (abs ((first :a) - (first :b))) + (abs ((last :a) - (last :b))))
end

to abs :num
ifelse :num < 0 [op -1 * :num] [op :num]
end

You can replace the above hypotenuse procedure with this, but realize that it will no longer calculate the straight-line distance between two points. It might be a good idea to change its name here and in herb and carn where it is called.

Addendum B

• Add these lines to setup

  getshapes
  make "carn.color 3
  make "herb.color 1
  make "plant.color 2

• Replace these lines in setup

  make "male char 11
  make "female char 12

  These replace m and f with the male and female signs.

• Add these lines to setup if you have EGA(16 color) or VGA(256 color) graphics

  make "carn.baby 11
  make "herb.baby 9

• Add these lines to setup if you have CGA(4 color) graphics

  make "carn.baby 3
  make "herb.baby 1

  Because there are only four pen colors with CGA, the offspring will be the same colors as their parents. This will lead to higher mating and feeding counts.

• Add these lines to setup if you have CGA or EGA graphics

  make "water.1 6
  make "water.2 10
  make "water.3 13
  make "water.4 5
  make "water.5 0

• Add these lines to SETUP if you have VGA graphics

  make "water.1 18
  make "water.2 17
  make "water.3 16
  make "water.4 5
  make "water.5 207
  

More shades of blue are available with VGA colors.

Addendum C

For Apple II LogoWriter Users

• Add these lines to setup

  getshapes
  make "carn.color 3
  make "carn.baby 4
  make "herb.color 1
  make "herb.baby 5
  make "plant.color 2
  make "water.1 0
  make "water.2 0
  make "water.3 0
  make "water.4 0
  make "water.5 0

• Replace these lines in setup

  make "width 280
  make "height 180
  

The screen heights and widths are smaller for the Apple II.

For Apple IIGS (with or without Ensemble) LogoWriter Users

• Add these lines to setup

  make "carn.color 3
  make "carn.baby 11
  make "herb.color 1
  make "herb.baby 9
  make "plant.color 2
  make "water.1 6
  make "water.2 10
  make "water.3 13
  make "water.4 5
  make "water.5 0

• Replace these lines in setup

  make "male char 11
  make "female char 12

  These replace m and f with the male and female symbols.
  

For Apple IlGS Non-Ensemble LogoWriter users

• Add this line to setup

  getshapes
  

Addendum D

• Do not type in the following procedures

  eat.count
  check.feedings
  circadian water
  rollover
  sq :num
  hypotenuse

• Add these lines to setup

  make "carn.color 2
  make "carn.baby 10
  make "herb.color 1
  make "herb.baby 15
  make "plant.color 3

• Delete these lines from setup

  make "eatcnt0 0
  make "eatcnt1 0
  make "eatcnt2 0
  make "eatcnt3 0
  make "day 1
  make "time 0
  make "meridian "AM
  make "h.births 0
  make "c.births 0
  make "male "M
  make "female "F
  setbg :water.5

• Delete this command from begin: circadian
  
• Delete this command from herb: eat.count
  
• Delete this command found in two places in carn: eat.count
  
• Delete this line from herb.mate: make "h.births :h.births + 1
  
• Delete this line from carn.mate: make "c.births :c.births + 1

• Add these procedures:

  to xcor
  op first pos
  end

  
  to ycor
  op last pos
  end
  

Use the second hypotenuse (Manhattan Grid Distance) procedure. There is no sqrt command in the Commodore 64's LogoWriter 1.1.

to abs :num
ifelse :num < 0 [op -1 * :num] [op :num]
end

to hypotenuse :a :b
op (abs ((first :a) - (first :b))) + (abs ((last :a) - (last :b))))
end

Addendum E

• Add these lines to setup

  make "carn.color 6
  make "carn.baby 37
  make "herb.color 8
  make "herb.baby 9
  make "plant.color 3
  make "water.1 171
  make "water.2 188
  make "water.3 208
  make "water.4 242
  make "water.5 180

• Replace these lines in setup

  make "width 495
  make "height 220
  

The screen heights and widths are larger for the Macintosh.

Shape Variable :plant.sh :herb.m.s :herb.f.s :herb.b.s :carn.m.s :carn.f.s :carn.b.s	Shape 1 3 4 5 6 7 8	Object Category plant male herbivore female herbivore baby herbivore male carnivore female carnivore baby carnivore	My Simulation grass fish fish fish fish fish fish	Student Simulation tree giraffe giraffe giraffe lion lioness lion cub

Table 2: Turtle Identities

Turtle Number 0 1 2 3	Identity male herbivore male carnivore female herbivore female carnivore

Color-Variable :carn.color :herb.color :plant.color :carn.baby :herb.baby :water.1 :water.2 :water.3 :water.4 :water.5	IBM-CGA magenta-3 white-1 cyan-2 magenta-3 white-1 brown-6 lt cyan-10 lt blue-13 blue -5 black -0	IBM-EGA magenta-3 white-1 cyan-2 lt magenta-11 t gray-9 brown-6 lt cyan-10 lt blue-13 blue -5 black-0	IBM-VGA magenta-3 white -1 cyan-2 lt magenta-11 lt gray-9 lavender-18 med. blue-17 lt blue-16 blue-5 dk purple-207	Macintosh magenta-6 lt gray-8 green-3 lt magenta-37 gray-9 lt blue-171 bl-green-188 grn-blue-208 dark blue-242 lt purple -180	Apple-IIGS magenta-3 white-1 cyan-2 ltmagenta-11 lt gray-9 brown-6 lt cyan-10 lt blue-13 blue-5 black -0	AppleII purple-3 white-1 green-2 orange-4 blue-5 black-0 black-0 black-0 black-0 black-0	C 64 red-2 white-1 cyan-3 pink-10 gray-15

Color Number 0 1 2 3 4 5 15	Color black white cyan magenta red blue light green

Addendum F

This is an edited version of the program written by The EcoGroup. (The EcoGroup: Sandy Cid, Vanessa Cook, Kristina Negron, Maritza Schaeffer, and Laura Stickney Class of 1999 St. Hilda's & St. Hugh's School) I have removed all of their predetermined scenarios for the sake of space and simplicity.

to startup
getshapes
scenery
setup
move
end

to scenery
scene
pond
trees
sun
end

to scene
rg
setbg 15
setc 5
rt 90
fd 320
pu
lt 90
fd 15
pd
fill
end

to pond
pu
home
bk 30
rt 90
fd 145
setsh 12
setc 5
repeat 6 [lt 60 fd 7 pd stamp pu]
end

to trees
pu
home
bk 45
rt 90
setsh 1
setc 2
repeat 12 [pd stamp pu fd 32]
fd 16
lt 90
bk 20
rt 90
repeat 12 [pd stamp pu fd 32]
end

to sun
pu home
rt 90
fd 120
setsh 12
setc 4
lt 90
fd 68
pd
stamp
end

to setup
tell all
st
pu
home
tell [0 2]
setc 1 seth 90
tell [1 3] setc 3
seth 270
tell 0 setsh 3
tell 1 setsh 6
tell 2 setsh 4
tell 3 setsh 7
end

to move
tell 0 herb
tell 1 carn
tell 2 herb
tell 3 carn
move
end

to carn
fd random 10
seth 248 + random 45
if equal? colorunder 1 [eat]
if equal? colorunder 3 [c.mate]
if ycor > 0 [descend]
if ycor < -80 [ ascend]
end

to herb
fd random 10
seth 68 + random 45
if equal? colorunder 2 [eat]
if equal? colorunder 1 [h.mate]
if ycor > 0 [descend]
if ycor < -80 [ ascend]
end

to eat
pe
fill
pu
end

to c.mate
tell 3
setsh 8
pd
stamp
pu
setsh 7
fd 20
end

to h.mate
tell 2
setsh 5
pd
stamp
pu
setsh 4
fd 20
end

to descend
seth 180
repeat 20 [fd 1]
end

to ascend
seth 0
repeat 20 [fd 1]
end

As stated earlier, if you want to test for distance rather than colorunder (you must on the Macintosh and Commodore 64), you will need to replace if colorunder = 1 [h.mate] in herb with:

ask 0 [make "pos0 pos]
ask 2 [make "pos2 pos]
if ((hypotenuse :pos0 :pos2) < 16) [h.mate]

In carn you will need to replace if colorunder = 3 [c.mate] with:

ask 1 [make "pos1 pos]
ask 3 [make "pos3 pos]
if ((hypotenuse :pos1 :pos3) < 16) [c.mate]

You will then need to add the hypotenuse and sq procedures for straight-line distance (not for the C64), or hypotenuse and abs for Manhattan Grid Distance, found on the last page of my program listing.

Figure 9: Ecology Simulation Flow Chart

start
setup
set.grass
grow.grass
plant.grass
set.fish
begin
herb
feed
eat.count
check.feedings
labor
descend
give.birth
birth.check
swim
hypotenuse
sq
herb.mate
give.birth
birth.check
swim
swim.test
swim
carn
feed
eat.count
check.feedings
labor
ascend
give.birth
birth.check
swim
hypotenuse
carn.mate
give.birth
birth.check
swim
swim.test
swim
circadian
water
rollover
random.grass
set.grass
plant.grass
begin
end