Iteration is ideal work for a computer and it's
quite worthwhile for folks embarking on the study of chaos to
see some basic computer code.
A natural way to perform iteration in Javascript (and many other
computer languages) is with a loop. If you just want to iterate
a certain number of times, a for loop is probably
the easiest way to go. I guess the code should look like this:
for(i=0; i<bail; i++) {
'do something'
}
If bail is set, that little snippet should
execute 'do something' that many times. Of course,
'do something' should do something, rather than
nothing. In our case, we'd like to apply a function to a
previously defined value and push the result onto a list.
The whole thing might look like so:
x = x0; // Starting point
list = [x0]; // Initialize the list
for(i=0; i<bail; i++) {
x = f(x); // Compute the next value
list.push(x); // push the next value onto list
}
list // return the result
If x0, bail, and f
are defined, that code should run perfectly and generate the
result of iterating f a total of
bail times
starting from x0.
You can try this in the little textarea below which is set up to
accept code written in Javascript. Any code whose final result is an
array of numbers should do. It could literally be as simple as
[1,2,3] but our objective here is to study iteration.
For those who don't know Javascript,
the examples menu provides a start illustrating the ideas above.
Those examples can be edited however you like.
For those who do know Javascript, note that all the symbols
from the Math namespace have been imported into the global
namespace. This allows you to abbreviate a function like
Math.cos(Math.PI*x) as just cos(PI*x).
After you have an example, hit the generate button to automagically
generate a timeseries plot and a table of the orbit.
Once you feel like you understand the examples, you can edit them just a little bit to change the function, starting point, or number of iterates. At some point you should try out your personal logistic function.