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Real Function Iterator


This applet requires the use of a digital signature/certificate in order to save screenshots of graphs generated by the applet. When asked for your approval, you should run/trust the certificate.

Download a copy of Real Function Iterator for your computer here and see version history here.


This applet iterates any real function, and displays the orbit as a numerical list and as points on a number line. It allows the user to choose up to three seed values at a time and view their orbits.

Basic Operation

By entering a function f(x) either by typing it in (with help from the Function Help drop down menu) or by selecting one from the drop down menu of Pre-selected functions) and then clicking the Graph f(x) button, the user will see the graph of f(x) appear in the Viewing window. By clicking on the graph of f(x), a seed 1 value x_0 will be selected. One can also type in the seed 1 value x_0 directly and then click the Update button. One can then iterate f(x) by clicking on the + button next to Iterate f(x) (or iterate 10 or 50 steps at a time with the corresponding buttons). The successive orbit values are then plotted and also displayed in a table. (These values can be copied and pasted into another file in the usual way, if one wishes to.) By typing in a value for n and clicking on the + button next to Iterate f(x), the user can produce the first n orbit points x_1,..., x_n. The - button will allow the user to reverse the process, one step at a time. Also, by checking the boxes Show seed 2 and Show seed 3, one can choose multiple seed values to be iterated simultaneously.

Zooming on pictures

Zooming on any graph can be done by in a variety of ways.

  • Depressing the mouse and dragging it across the graph zooms in.
  • Right/left click on the graph zooms in/out (user will have to first check the Zoom with mouse click on).
  • Moving the slider on the zoom panel with a mouse drag or the right/left arrows on the keyboard zooms in/out.

The last two methods of zoom can either be centered at the cursor or at a preset default point (set to (0,0) in the above screen shot). Ctrl+click in viewing window will reset zoom center to the cursor value.

For all zoom methods, the Default View button will return the viewing rectangle to the default setting. Default settings can be changed by selecting one from the drop down menu just above the viewing window. The user can also choose their own viewing window parameters by typing in the horizontal and vertical ranges manually. This view can then be set as the default by selecting Capture view in the drop down menu. Crossed or boxed axes may be selected with the buttons labeled as such.

Exporting pictures and Applet Settings

At the top left of the applet are the following drop down menus:

  • Export will allow the user to save a png, gif, or jpg picture of the either the whole applet or the viewing window (Graph).
  • Graph settings will allow the user to adjust various settings such as axes style and color.
  • Colors will allow the user to adjust the color of the text used in the headings of the various sections of the applet.


This material is based upon work supported by the National Science Foundation under Grant No. 0632976.

Version 1.3 (with menu bar).