This function can be used to generate spiderweb plots for continuous maps of the interval [0 1] into itself.
This type of graph is used to visualize successive iterations of an interval map f. Given an initial point x0, the segments that make up the diagram connect the points
(x0, f(x0)), (f(x0), f(f(x0))), (f(f(x0)), f(f(f(x0)))), ...
The arguments for SPIDERWEB are the following:
1. f - a continuous map of the interval [0 1] into itself. Maps that do not take the interval [0 1] back into itself may not produce the correct spiderweb plot.
2. x0 - the initial point.
3. N - the number of iterations. SPIDERWEB computes the forward trajectory of length N for the point x0. These points are stored in the vector xIm = X-IMAGES, so that xIm = [ x0 f(x0) ... (f^N)(x0) ]
Examples and sample function calls:
The following examples appear in the H1 line of the function.
1. The symmetric tent map:
>> f = @(x) (2*x).*(x<0.5) + (2-2*x).*(x>=0.5);
>> spiderweb(f, 0.124, 50);
2. The standard quadratic (logistic) map:
>> f = @(x) (4*x).*(1-x);
>> xIm = spiderweb(f, 0.12, 50)
Create scripts with code, output, and formatted text in a single executable document.