This is the column of 2 radio buttons entitled "Plot Mode:" at the top right of the control panel area. In line graph
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 spot value
mode, the spot value of x 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 spot value
mode, the Scan Mode is automatically set to continuous
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 line graph
mode when continuous
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 beneath the title "Adjust 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 0·01 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 not
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 allows 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 0·01 (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