Fixed points and lamerey diagrams, how to implement in matlab?

Question

MATLAB

One of the theorems of mathematical analysis states that xn → xf , where xf is a fixed
point. The process of convergence of a sequence to a fixed point can be depicted
graphically using the so-called spider diagrams (or Lamerey diagrams) (you
may still meet them in the course of control theory).
The web diagram is constructed as follows. Let's take the sequence constructed according to the above rule: x0, x1, x2, . . . , xn. We construct the starting point
(x0, x1), connect it to the point (x1, x1), connect this point to (x1, x2), this point to (x2, x2), etc. In
the general case, at each step we move from point (xk−1, xk) to point (xk, xk) and then
to (xk, xk+1).
Your task: according to the described algorithm, construct the function [X, Y] = findFixedPoint(f,
initPoint, N). The first argument to this function is a variable containing the anonymous function for which the fixed point is built. The second argument to this function
is the starting point x0. The third argument is the number of iterations (that is, the length of the sequence {xn}). The function must return two vectors, x and y, containing the corresponding coordinates of the nodes of the polyline. In addition to the function, you need to write a script that uses findFixedPoint and builds a Lamerey diagram for the given function.
Your function for which you will write the script is
f(x) = 4 cos 3x Plotting
interval: x ∈ [−1; one]. x0 must also belong to the given
interval. The line y = x and the function y = f(x) must also be present on the chart.
The chart should be titled and the axes labeled.