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3D Surface

 If you download the NetLogo application, this model is included. You can also Try running it in NetLogo Web

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.

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Please cite the NetLogo software as: