WHAT IS IT?
-----------
This model is an extension of a previous StarLogo project
called "Kaleidoscope". The current version has added six
new patterns. The name of this model is called Geometron-Top-Down.
HOW TO USE IT
-------------
Set NTURTLES to a desired value between 0 and 360 (default value is 20).
NTURTLES determines how many initial turtles you want to start out with.
These initial turtles will spawn other shape-making turtles.
Set COLOR-SEP to a desired value between 0 and 60 (default value is 12).
COLOR-SEP determines the range of colors that the turtles (and hence the
kaleidoscope) will take on. The higher the value, the smaller the range.
When you have set COLOR-SEP and NTURTLES, press the
SETUP button to set-up the model.
Next, choose a pattern. In each pattern, the initial turtles hatch other
turtles and those hatched turtles draw different geometric shapes. Each
pattern is represented by a forever button. The user cannot change
PATTERN-2, PATTERN-4 or PATTERN-6. PATTERN-1, PATTERN-3, and PATTERN-5,
however, allow for user control using the DIRECTION and EXPANDER sliders.
For detailed descriptions of the instructions in each pattern, go to the
end of the info-window.
The slider DIRECTION (default value is 2) is designed for PATTERN-1 and
PATTERN-3. At each cycle, DIRECTION determines the amount that the
pattern-making turtles turn to the right. In other words, if DIRECTION
is set to 12, each turtle will turn 12 degrees to the right before moving
forward.
The slider EXPANDER is designed specifically for pattern 5 (default value
is 80). At each cycle of PATTERN-5, EXPANDER determines how large each
leg of the polygon will be.
The user also has control over the color distribution
exhibited by each pattern. The COLOR-SHIFT button will
continuously increase or decrease the value of
'curr-color-sep' by a small random amount.
(Thus the slider value itself isn't changed, but the color value of the
turtle is.) The INC-DEC-COLOR switch determines if 'curr-color-sep' is
increased or decreased.
Other added features of the model are the CLEAR-PATCHES-LIFT-PEN and
RESTORE buttons. CLEAR-PATCHES-LIFT-PEN does exactly what it says: it
clears the screen of all patches, lifts the pen on all turtles and kills
all turtles greater than NTURTLES. RESTORE kills all turtles greater
than NTURTLES and tells all turtles to put their pen down. Killing all
turtles greater than NTURTLES restores the original number of turtles on
the screen.
A useful tool that can be used in conjunction with the
CLEAR-PATCHES-LIFT-PEN and RESTORE buttons is a switch called
FOLLOW-TURTLE. When you CLEAR-PATCHES-LIFT-PEN, you see the skeleton of
the pattern since the turtles are moving without their pen down. But when
the switch is turned on, one hatched turtle will put its pen down.
However, since turtles are constantly being born and dying it may take
time for this particular turtle to appear. It should also be understood
that because some of the patterns divide the turtles into different
groups and assign them different shapes to create, more than one turtle
may be told to put its pen down in order to represent what all the
turtles in the pattern are doing.
Two monitors are provided at the bottom of the Interface
Window. COUNT-TURTLES displays the current number
of turtles on the graphics window. Likewise, CURR-COLOR-SEP displays that
variable's value, so that you know when it has been altered, and by how
much.
THINGS TO NOTICE
----------------
An important thing to notice here is the number given in
COUNT-TURTLES. Right away, it becomes much larger than
NTURTLES, but quickly settles on some nice big number. Take a look at the
Procedures Window. Initially, upon setup, there are NTURTLES turtles.
Once one of the
pattern buttons is pressed, each of these turtles repeatedly hatches a
new turtle and turns by a specified degree.
It is important to understand that this phenomenon, the fact that initial
NTURTLES is exploding into a number much larger than NTURTLES is because
other turtles are being hatched in between the time a single turtle is
hatched and the time it finishes drawing its given shape. Thus, if we
were to add a wait statement into one of the patterns, not as many
turtles could be hatched. In other words, the number of turtles greater
than NTURTLES would decrease. As turtles execute their commands much
quicker than the hatched turtles, they produce many turtles during one
loop of a pattern; eventually, though, turtles start to die off. At this
point, the number of turtles who are born is roughly equal to the number
who die at any given step.
You also should notice how COLOR-SEP (known in the code as
'curr-color-sep') alters the appearance of the pattern.
Turn COLOR-SHIFT on, and let 'curr-color-sep' become very
large. Then watch what happens when it is small, maybe zero or some
negative number.
THINGS TO TRY
-------------
Try playing around with the DIRECTION slider on PATTERN-1 AND PATTERN-3
and the EXPANDER slider on PATTERN-5. Observe what happens to the
pattern as you change the values of each.
GEOMETRON-TOP-DOWN is meant to be a visually pleasing model just to
watch. See what different values of
COLOR-SEP produce, and explore how COLOR-SHIFT changes the
appearance of the kaleidoscope. What seems the best to you?
Try changing the code in the Procedures Window. Increase the size of the
shapes drawn by each of the turtles, or try changing the size of the
angle each of the turtles turns through.
Instead of each turtle moving or turning a given amount,
what about having it move a small random amount (as in the
changes to curr-color-sep from COLOR-SHIFT). How much
randomness can you add to 'kaleidoscope' and still maintain some kind of
overall structure?
After running one of the patterns, try changing the number
of NTURTLES and then stop the pattern and push CLEAR-PATCHES-LIFT-PEN.
Then start the pattern again. What happens? Can you explain why this
happens?
EXTENDING THE MODEL
-------------------
Whenever a turtle is hatched by one of NTURTLES, it
proceeds to draw a certain pattern. Change the 'hatch' command list so
that it draws some other shape or pattern. Try to predict what overall
shape will emerge.
Try to write an entirely new kind of GEOMETRON-TOP-DOWN project. In the
current project, turtles spin off from a center core of NTURTLES turtles.
In your new project, maybe the drawing turtles could orbit around some
fixed (or moving) point-look at the StarLogo projects 'n-bodies' and
'gravitation'.
STARLOGOT FEATURES
-----------------
GEOMETRON-TOP-DOWN makes nice use of the turtle primitive
'hatch'. Whenever a turtle is hatched, it executes the
command list that follows the 'hatch' command. Generally all it does is
change its color or alter some variable- there's no reason it can't run
some other, possibly lengthy, procedure. (Which is exactly what happens
here.)
NOTES ON THE SHAPES
---------------
The following is a list of all the basic shape functions that are used in
this model to create the six patterns. It is important to understand
that the complexity of the patterns are actually nothing more than
different combinations of these shape functions. For example, pattern-1
utilizes the rigth-shape and left-shape functions. Both these functions
simply draw circles. However, by adding slight variations to what the
turtle does and which ones do it, it is possible to create the pattern
that is represented by pattern-1. This, in fact, is the basic algorithm
that the model uses in order to create all the patterns. Take the basic
shape functions, add slight variations to what the turtles do and choose
which turtles do it.
RIGHT-CIRCLE
-----------
Performs the following procedure 180 times:
Move forward 1.5 steps and turn right by 2 degrees.
To see the shape that this function creates, try calling it in the
command center with one turtle with the pen down.
A turtle will create a circle heading in the right direction.
LEFT-CIRCLE
-----------
Performs the following procedure 180 times:
Move forward 1.5 steps and turn left by 2 degrees.
To see the shape that this function creates, try calling it in the
command center with one turtle with the pen down.
A turtle will create a circle heading in the left direction.
LEFT-SQUARE
-----------
Performs the following procedure 4 times:
Move forward EXPANDER steps and turn right by 90 degrees.
To see the shape that this function creates, try calling it in the
command center with one turtle with the pen down.
A turtle will create a square heading in the left direction.
RIGHT-TRIANGLE
--------------
Performs the following procedure 3 times:
Move forward 35 steps and turn right by 120 degrees.
To see the shape that this function creates, try calling it in the
command center with one turtle with the pen down.
A turtle will create a triangle heading in the right
direction.
OCTAGON
--------
Performs the following procedure 8 times:
Move forward 30 steps and turn right by 45 degrees.
To see the shape that this function creates, try calling it in the
command center with one turtle with the pen down.
A turtle will create an octagon heading in the right
direction.
PENTAGON
---------
Performs the following procedure 5 times:
Move forward 35 steps and turn right by 72 degrees.
To see the shape that this function creates, try calling it in the
command center with one turtle with the pen down.
A turtle will create a pentagon heading in the right
direction.
HEXAGON
--------
Performs the following procedure 6 times:
Move forward 30 steps and turn right by 60 degrees.
To see the shape that this function creates, try calling it in the
command center with one turtle with the pen down.
A turtle will create a hexagon heading in the right direction.
NINE-GON
---------
Performs the following procedure 9 times:
Move forward 35 steps and turn right by 40 degrees.
To see the shape that this function creates, try calling it in the
command center with one turtle with the pen down.
A turtle will create a nine-gon heading in the right
direction.
SLIDER DESCRIPTIONS
-------------------
EXPANDER
--------
Numbered from 0 to 90 and increments by 1. Expands and
contracts the square created by LEFT-SQUARE. Associated with
PATTERN-5.
DIRECTION
---------
Numbered from 0 to 10 and increments by 0.1 or (1/10). Turns
a turtle to the right by the number of degrees specified by
the slider. Associated with PATTERN-3 and PATTERN-1.
WHAT THE PATTERNS DO
----------------------------
PATTERN-1
----------
In this pattern, every 10th turtle moves forward .5 steps and to the
right by DIRECTION degrees. Each call to the pattern hatches a turtle
who performs the RIGHT-SHAPE function, then the LEFT-SHAPE function and
then dies. By increasing the DIRECTION, the turtles increase the degrees
by which they turn to the right. This means that at each forward
movement the turtle turns tighter around a center point. Thus, when
DIRECTION is set to 0, the turtle simply moves forward. The more it is
increased, say from 0 to 1 to 2 to 10, the more circular the turtles
movement becomes. Although the pattern changes, it must be understood
that the underlying shape that is being created is a circle.
PATTERN-2
----------
Every even numbered turtle moves forward 1 step and turns right by 1
degree. It then hatches a turtle that performs the HEXAGON function and
then dies. Every odd numbered turtle moves forward 1 step and turns left
by 1 degree. It then hatches a turtle that performs the OCTAGON function
and then dies. It is interesting to note that when the nturtles slider
is raised to a high number ,i.e., greater than or equal to 200, the
pattern in the lower numbers becomes unrecognizable. However, it must be
understood that although the new pattern may appear to be different,
still, the underlying shapes that are being made are the hexagon and
octagon.
PATTERN-3
----------
Every 5th turtle moves forward .5 steps and turns right by DIRECTION
degrees. It then hatches a turtle which performs the PENTAGON function
and then dies. PATTERN-3 and PATTERN-5 are probably the simplest
patterns in this model in terms of explaining their behavior. Basically,
PATTERN-3 creates pentagons, but because the turtles move forward .5 and
move to the right DIRECTION number of degrees, this is what causes the
pattern to drastically change. The illusion is that the hatched turtles
are somehow creating different shapes but the truth of the matter is that
they are making pentagons and always will be making pentagons. It is
only the slight variations in outside influences that brings about a
change in the pattern.
PATTERN-4
----------
Every 3rd turtle turns right by 1 degree and then hatches a turtle that
performs the NINE-GON function and then dies. All the other turtles turn
left by 1 degree and then hatch a turtle that performs the LEFT-SHAPE
function and then dies.
PATTERN-5
----------
Every turtle hatches another turtle that performs the LEFT-SQUARE
function and then dies.
PATTERN-6
----------
Every turtle moves forward DIRECTION steps and then hatches a turtle
which performs the following functions in the following order: NINE-GON,
OCTAGON, RIGHT-SHAPE, PENTAGON, HEXAGON, and LEFT-SHAPE. After
performing these functions, each hatched turtle then dies.
IMPORTANT NOTES
************************************************************
Notice that in each of these functions, the number of times the
procedure is repeated multiplied by the number of degrees the turtle
turns either to the right or to the left is equal to 360 degrees. Which
means that each of the turtles is creating a polygon.
I discovered that in the patterns where the turtle moves a number of
steps forward and then turns right or left in some direction, this action
significantly changes the pattern. For example, in pattern-1, the fact
that each hatching turtle moves .5 steps forward means that the resulting
shape from the RIGHT-CIRCLE OR LEFT-CIRCLE function will resemble a
kidney bean rather than a circle, which is what the RIGHT-CIRCLE and
LEFT-CIRCLE function are designed to produce.
It is important to understand that these patterns are able to be
created because they obey certain basic rules about geometry. For
example, I mentioned above that all the functions create polygons. This
is due to the fact that every polygon must have the interior sum of its
angles equal to 360 degrees. However, certain slight alterations like
those mentioned above, are enough to change the shape and create a new
one. For example, if the DIRECTION slider started off at 0 in pattern-1,
every hatching turtle would simple be moving forward by .5 steps as it
was creating its pattern. However, if we increase the slider by
increments of .1, we notice that its movements seem to be getting tighter
and tighter until it remains fixed in one place and keeps revolving
around a point.
************************************************************