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NetLogo Models Library:
Sample Models/Mathematics

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3D Surface

[screen shot]

If you download the NetLogo application, this model is included. (You can also run this model in your browser, but we don't recommend it; details here.)

WHAT IS IT?

This model maps turtles between Cartesian and spherical 3-dimensional coordinates. To create the appearance of a curved 3D surface, the program generates turtles with random x- and z-coordinates, then computes each turtle's y-coordinate based on x and z, and time. The cosine function is used in the formula to produce a curved surface. Varying the y coordinate based on time produces motion.

HOW IT WORKS

To render the surface in the NetLogo view, it maps from 3D to 2D coordinates as follows:

>view x = turtle x + (turtle z) / 2 >view y = turtle y + (turtle z) / 2

In other words, increasing z causes the turtle's apparent position to move both up and to the right.

HOW TO USE IT

Click the SETUP button to generate the turtles and place them on the surface. Click the GO (forever) button to run the model, which continuously varies the turtles' y-coordinates to generate a wavelike motion.

The NUM-TURTLES slider determines the number of turtles that make up the surface.

THINGS TO NOTICE

Notice that as the turtles move down (y-coordinate decreases) they become darker in color, and when they move up (y-coordinate increases) they become lighter.

THINGS TO TRY

Experiment with the NUM-TURTLES slider. How many turtles are needed to produce a realistic effect? Why doesn't it keep getting better-looking indefinitely as you add more turtles?

In the move procedure, try other numbers besides 5 in front of and inside the cosine function. Explain the new behavior!

EXTENDING THE MODEL

Try changing the formula used to compute the y-coordinate to produce differently shaped surfaces.

See if you can draw not just a surface, but a three dimensional shape such as a cone or a sphere.

NETLOGO FEATURES

Notice the use of scale-color to change a turtle's color based on its y-coordinate. Also see the model "Wave Machine" for a version that uses patches rather than turtles to make a 3-D membrane.

RELATED MODELS

3D Solids Wave Machine

HOW TO CITE

If you mention this model or the NetLogo software in a publication, we ask that you include the citations below.

For the model itself:

Please cite the NetLogo software as:

COPYRIGHT AND LICENSE

Copyright 1998 Uri Wilensky.

CC BY-NC-SA 3.0

This work is licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 License. To view a copy of this license, visit https://creativecommons.org/licenses/by-nc-sa/3.0/ or send a letter to Creative Commons, 559 Nathan Abbott Way, Stanford, California 94305, USA.

Commercial licenses are also available. To inquire about commercial licenses, please contact Uri Wilensky at uri@northwestern.edu.

This model was created as part of the project: CONNECTED MATHEMATICS: MAKING SENSE OF COMPLEX PHENOMENA THROUGH BUILDING OBJECT-BASED PARALLEL MODELS (OBPML). The project gratefully acknowledges the support of the National Science Foundation (Applications of Advanced Technologies Program) -- grant numbers RED #9552950 and REC #9632612.

This model was converted to NetLogo as part of the projects: PARTICIPATORY SIMULATIONS: NETWORK-BASED DESIGN FOR SYSTEMS LEARNING IN CLASSROOMS and/or INTEGRATED SIMULATION AND MODELING ENVIRONMENT. The project gratefully acknowledges the support of the National Science Foundation (REPP & ROLE programs) -- grant numbers REC #9814682 and REC-0126227. Converted from StarLogoT to NetLogo, 2001.

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