Getting Started: The Pisces Logo

In this section we describe how to compute the zero set of the default Pisces model. If you have never run Pisces, you may wish to read the section of documentation that describes how to launch Pisces.)

Upon beginning a new Pisces session, the main panel appears. Note that the default model is the Pisces Function, which means that this is the function for which Pisces will attempt to compute a level set.

Computing a Level Set

Open the control panel for the Adaptive Grid Algorithm by selecting the first entry on the Algorithms menu.
Press the Go button on the algorithm's control panel in order to request that Pisces use the adaptive grid algorithm (with the default parameters) to compute the level set of the current model.
Open a View Window by selecting the first entry on the Output menu. The window should contain the Pisces logo, which is actually the level set of an 11th degree polynomial in two variables.

Manually Changing the Viewport

Edit the bounds of the view window's viewport to [-5,5]x[-5,5] in order to change the way that the Pisces logo appears on your screen. (Hint: After changing the minimum value of the x variable to read -5, <TAB> to the next field. When you have changed the entire viewport, press <RETURN> to submit the changes.)

Zooming with the Mouse

To zoom in on the Pisces logo, position the cursor of your mouse at the upper left corner of the logo (just above the tail of the "upper" fish). Hold down the rightmost mouse button while you drag out a rectangle that contains the lower right corner of the logo. The "rubber-band box" should encompass most or all of the Pisces logo. Release the right mouse button and select Actions->Zoom in in order to scale everything that was inside the rubber-band box until it fills the viewport.

Restoring the Default Viewport

Select the menu item Actions->BBox->Viewport in order to restore the viewport to the domain [-2.2, 2.2]x[-1.2,1.2].

Modifying Model Parameters

Under the Settings menu on the main panel, choose the first item labeled Model. This action will create a new panel called the Model Panel. This panel enables the user to control each model's parameters, domain, and range. To see how this works, change the value of the parameter labeled eyerad to read 0.3. Compute the level set for this new function by pressing the Go button on the control panel for the Adaptive Grid Algorithm. The View Window should display a new image of two fish with big eyes. Because the fish eyes are almost touching the fish's "forehead," this function is nearly singular, and so the level set in the vicinity of the forehead will look as if the fish have been attacked by some kind of necrotic fungus.

Modifying Algorithm Parameters

To cure the Pisces logo of its "scale rot," change the parameter Max_Depth in the Adaptive Grid Control Panel so that the parameter has the value 15. Recompute the level set by pressing the Go button. After a few seconds, the fish will look much improved.

Printing

To print the big-eyed Pisces logo, open the Postscript Panel located on the Output menu of the Main Panel. On this panel, press the Print button to create a postscript file (called pisces.ps, by default). The file will appear in the directory from which you invoked Pisces, and may be sent to any postscript-compatible printer. On UNIX workstations, this is accomplished with the lpr command.

Ending the Session

If desired, change other parameters in the Model Panel and compute the related level set to get a feel for how the level set changes with the parameters. Similarly, change parameters that control the Adaptive Grid algorithm to see how each parameter affects the computation of the level set.

When you are finished, end this Pisces session by selecting Quit from the File menu on the Main Panel.

Next: A Family of Circles

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