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view/download model file: hw1-forrest.nlogo
WHAT IS IT?
-----------
The model displays two basic
conic sections: circles and ellipses. The figures are generated
behaviorally as opposed to algebraically -- the turtles attempt to
behave like points on the specified shape.
A circle is the
set of all points at a certain distance (radius) from a central
point. An ellipse is the set of points such that the sum of the
distances to two points is constant. These two points are called
foci. The CONSTANT slider corresponds to the radius for circles and
to the sum of distances to the foci for each turtle.
As an
illustration of this, imagine a string loosely looped around two
nails, each representing a focus. If you pull the string tight with a
pencil point and move the pencil point around the foci, you will draw
an ellipse.
The ancient Greeks discovered that each conic
section can be found by taking a cross section of one or two cones
with their points pointing toward each other. A circle results from
taking a slice that is perpendicular to the axis, while an ellipse
results from taking a slice of one cone that is not perpendicular to
the axis. Similiarly, a parabola results from a cross section that
passes through one cone in a vertical fashion, such that the plane of
the cut is parallel to one face. A hyperbola results from a vertical
section that passes through both cones.
The turtles use
feedback to make decisions about how they behave. They set out in
random directions, and then they receive information as to whether or
not they are getting closer to where they want to be. If they are
getting closer, they continue moving forward in the direction they
are going. If they are moving farther away, they set out in a new
random direction. This process is akin to the children's game of "Hot
& Cold", in which players are told whether they are getting
"hotter" or "colder" in relation to a hidden
goal.
HOW TO USE IT
-------------
*Circles:
-Select
the number of turtles with the TURTLES slider.
-Press SETUP.
-Make sure the SECOND-FOCUS switch is set to OFF.
-Press the
MOVE-TURTLES button. Adjust the radius of the circle with the
CONSTANT slider. The turtles will automatically correct themselves as
you change both CONSTANT and the location of the center. You can
change the circle's center by clicking on a new point.
*Ellipses:
-Select the number of turtles with the TURTLES slider.
-Press
SETUP.
-Make sure the SECOND-FOCUS switch is set to ON.
-Press
the MOVE-TURTLES button. As for a circle, the size of the ellipse can
be modified with CONSTANT, and new foci can be picked by clicking the
mouse.
THINGS TO NOTICE
----------------
When forming
a circle, turtles try to attain a distance of CONSTANT (a value
determined by the user with a slider) from a center that the user
determines by pointing and clicking (as explained above).
When
forming an ellipse, turtles try to attain a combined distance of 2 *
CONSTANT from the two foci, again determined by the user's points and
clicks. If the foci are too far apart, there be no way to satisfy
this condition. What do the turtles do then?
THINGS TO TRY
-------------
You may be able to get a better feeling for the
turtles' behavior if only a few turtles are on-screen at one time.
Try setting num-turtles to a smallvalue (like 16 or 1) and watching
the turtles.
Both of these conic sections can be observed by
shining a flashlight at a cone and looking at its shadow. Can you
figure out at what angles the cone must be held?
EXTENDING
THE MODEL
-------------------
If you have access to StarLogoT
(NetLogo's Macintosh-only predecessor), look at the StarLogoT model
'emergent-circle'. Watch how the turtles react with each other-
something that is missing from 'Conic Sections'. Implement this
emergent behavior for one or both of the conics in this project.
NETLOGO FEATURES
-----------------
Like more
traditional programming languages (e.g. C++), NetLogo can have
functions that report a value to the caller. The function used here
is called 'location'-- it has two inputs, an x-coordinate and a
y-coordinate. In this model, it reports true or false. It is set up
using "to-report" and "report".
CREDITS
AND REFERENCES
----------------------
To refer to this model
in academic publications, please use: Wilensky, U. (1998). NetLogo
Conic Sections model.
http://ccl.northwestern.edu/netlogo/models/ConicSections. Center for
Connected Learning and Computer-Based Modeling, Northwestern
University, Evanston, IL.
In other publications, please use:
Copyright 1998 by Uri Wilensky. All rights reserved. See
http://ccl.northwestern.edu/netlogo/models/ConicSections for terms of
use.
Back to Forrest's NetLogo Main Page.