is the collection of buttons etc. in the bottom left quarter of the applet's display area.
This is the column of 5 radio buttons entitled "Plot every:" at the extreme left of the control panel. It allows you to set or change the speed at which the applet iterates the equation and plots the resulting new value of x. The buttons are labelled in terms of the inter-plot
in milliseconds rather than the frequency of plotting. You can change the speed of plotting by clicking on one of these radio buttons. You may change the plot speed when the graph is stopped or while it is running. The change is effected immediately one of the radio buttons is clicked. The default speed is the fastest (a new value of x is plotted every 100 milliseconds) to give a sense of the process's rhythm. By slowing the process right down to a plot every 2 seconds you are better able to see the correlation between what is happening on the bounce graph and what is taking place on the time line graph.
This is the column of 2 radio buttons entitled "Equation:" at the top right corner of the control panel area. It allows you to select or change the equation you would like to exercise. You select the equation you want by clicking the appropriate radio button. Selecting the other (or even the same) equation causes the iteration process to reset itself. This causes each graph to be cleared of any existing trace and the constant c and variable x to be reset respectively to their default and starting values for the selected equation. After a reset the iteration process must be re-started by clicking the Start button.
Scan Mode Selector
This is the column of 2 radio buttons entitled "Scan Mode:" at the middle right of the control panel area. It allows you to set or change the scan mode. In
mode the process carries on iterating the selected equation until it gets to the end of the time line graph's time axis. The process then stops. This allows you to study the start-up and first 70 or so iterations of the equation. In
mode the iteration process carries on indefinitely. In this mode, when the time line graph has reached the end of the time axis, it flies back to the beginning again and continues plotting. In doing so it wipes the old trace a little distance ahead of each new plot. You can use the Stop button to temporarily halt the iteration process any time. The Start button then re-starts the iteration process from exactly where it was halted. You may if you wish change the scan mode while the equation is iterating.
Plot Mode Selector
This is the column of 2 radio buttons entitled "Plot Mode:" at the bottom right of the control panel area. In
mode, the Time Graph is plotted by joining consecutive plots with straight lines. This is the way you see the Time Graph being plotted when you first see the applet. In
mode, the spot value of x at after each iteration of the equation is displayed as a short horizontal line. Its length is that of the iteration period on the time axis. When you select
mode, the Scan Mode is automatically set to
so that plotting continues even after the plots have reached the end of the time axis. However, the trace does not then fly back to the beginning of the time axis as it does in
scanning is selected. Instead, it carries on plotting the values of x at the same horizontal position at the end of the time axis. These plots gradually build up into a 'bar' which shows the envelope within which the values of x vary once it has settled down after its initial 70 or so iterations from its starting value. This envelope is unique for each value of 'c' within the currently selected equation.
The 'Constant c' Entry Field
This is a text entry field in which you can enter your own value for the constant 'c' in the currently selected equation. It thus allows you to explore the effects of very small and precise changes in the value of 'c'. This is particularly interesting for the values around which the behaviour of the iterating equation changes dramatically from smooth to oscillatory or from oscillatory to chaotic. If you enter a collection of characters which cannot be parsed into a number within the valid ranges for 'c', the applet will reinstate the previous valid value. To enter a new value of c, click into the text field to the right of the title "Constant c", delete what is there already, type in the value you want and hit the 'return' key (on your computer's keyboard). The new value is then in effect. Entering a new value of c causes each graph to be cleared of any existing trace and x to be reset to its appropriate starting value. The iteration process must then be started by clicking the Start button.
The + - Buttons
These allow you to inch the value of 'c' up and down by .01 per click. However, they will not allow you to raise or lower 'c' outside its valid range of values for the currently selected equation. When you click either of these buttons the parabola on the bounce graph to the right expands or contracts accordingly to accommodate the new value of c.
The Stop/Start Button
The Stop button simply halts the iteration process at the point it has reached at the time. It does
reset x or c. Nor does it clear the graphs. Once the Stop button has been pressed, it turns into a Start button. As a Start button it simply re-starts the iteration process from the point at which it was stopped. This button thus allow you to stop the process and study the behaviour of the currently selected equation over any short snap-shot of time no matter how long the iteration process has been running. You may then restart the iteration process again if you so wish.
The 'Clear' Button
This causes the iteration process (if running) to be stopped and the graphs to be cleared. The value of x is reset to its starting value. If x = cx(1 - x) is the currently selected equation, the starting value for x is reset to a small arbitrarily value of .01 (otherwise x would never get off the ground). If x = x² + c is the currently selected equation, x is reset to zero. The Reset button does not alter the value of c.
| © June 1997 Robert John Morton