Interactivate: Two Variable Function Pump

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Two Variable Function Pump: Enter two complex numbers (z and c) as ordered pairs of real numbers, then click a button to iterate step by step. The iterates are graphed in the x-y plane and printed out in table form. This is an introduction to the idea of prisoners/escapees in iterated functions and the calculation of fractal Julia sets.

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Two Variable Function Pump: Enter two complex numbers (z and c) as ordered pairs of real numbers, then click a button to iterate step by step. The iterates are graphed in the x-y plane and printed out in table form. This is an introduction to the idea of prisoners/escapees in iterated functions and the calculation of fractal Julia sets.

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Two Variable Function Pump: Enter two complex numbers (z and c) as ordered pairs of real numbers, then click a button to iterate step by step. The iterates are graphed in the x-y plane and printed out in table form. This is an introduction to the idea of prisoners/escapees in iterated functions and the calculation of fractal Julia sets.On a mission to transform learning through computational thinking, Shodor is dedicated to the reform and improvement of mathematics and science education through student enrichment, faculty enhancement, and interactive curriculum development at all levels. Student development of numerical models and simulations integrated with core curriculum provides an opportunity to gain practical experience in computational science. Additionally, the National Computational Science Institute (NCSI) provides nation-wide workshops portraying resources and instructional ideas to middle school, high school, and undergraduate instructors for use in the classroom. Resources and materials offered to these instructors are available free of charge from Shodor's website and are largely developed by Shodor student interns. Shodor's academic program efficiently guides participants from excitement to experience to expertise through computational explorations, research opportunities, and service.We're sorry!We have detected JavaScript as being disabled in your browser.

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Printing Instructions
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The output of the activities in Shodor's Interactivate are created dynamically by computer languages such as Java. As a result, the pictures on the screen are not something that your browser can easily print. These instructions should enable you and your students to print out results from your explorations, to annotate them, and to make them part of any assessment.

Instruction for Windows Users

Please make sure that the image that you wish to print is visible on the screen.
Hit the "Print Screen" key on your keyboard. (This copies an image of your screen onto your computer's clipboard)
Open a writing or drawing program (such as Microsoft Word or "Paint")
- Paint can be found at: · All Programs · Accessories · Paint
"Paste" the image from the clipboard into the application (Edit · Paste).
If you're using "Paint": you can use the "crop" tool to keep only the part of the image you wish. To use the crop tool: select the part of the image you wish to keep, then select the "Cut" option from the file menu and open up a new window and select the "Paste" option.
Now you may print the file using File · Print.

Instruction for Mac OS Users

Press the following keys at the same time.
Command (aka. the flower/Apple key) · Shift · 4
You will notice that your mouse cursor becomes a cross-hair. Using the cross-hair, create a rectangular box around the image you wish to caputure, then release the mouse. If you make a mistake, while still pressing down on the mouse key, hit the ESC key.
A file will be created on your desktop called "Picture Y", where "Y" represents a number.
You can open this file in Preview and print from this program as normal.

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