The FORM portion is entered as TEXT, and the "NAME" is actually a variable called data that the second program will use to learn what value was entered by the user.
<HTML> <BODY BGCOLOR = "#FFFFFF"> <CENTER> <H1> Iteration Program </H1> </CENTER> Today's Date: <? print(date("l F d, Y")); ?> <H3> Enter a Value to Iterate </H3> <FORM ACTION = "results.php3" METHOD = POST> <INPUT TYPE="text" NAME = "data"> <P> <INPUT TYPE="submit" VALUE = "Show Results"> </BODY> </HTML>
<HTML> <BODY BGCOLOR = "#FFFFFF"> <CENTER> <H1> Iteration Results </H1> </CENTER> <B>Here are 10 iterations of the formula: <BR> y = x <SUP> 2 </SUP> </B> <P> <!-- PHP Calculations start here! --> <? $num = $data; print("Original value of x: <B>$data </B> <P>"); for($i = 1; $i <= 10; $i++) { $num = $num * $num; print("$i. $num <BR>"); } ?> </BODY> </HTML>
This program should request information such as the initial value of x as well as the rate constant, k, and possibly the number of iterations desired. A display will be generated that shows what happens as the equation, y = k*x*(1-x) is iterated, where 0 < x < 1 and 1 <= k <= 4.
Investigate different values of k to see if you can determine the exact point when the first Bifurcation happens. Can you find the second?