function webFixPt
%matlab code by Ed Greco 06/09/19
%HW Problem 26.1-----
%A) generate f(x) = lambda - x^2 
%   and plot web graph of convergance to an attractive fixed point.
%   export figure as .eps manually

lambda = .6; % less than 3/4 bifurcation value
Xmax = lambda*(1.05); % axis a bit higer than max of f(x)
Xall = (0:0.01:Xmax); % points to plot parabola (seems too many)
x(1) = .6;
num_iter = 30; %the number of times to iterate
for i = 1:2:num_iter
  x(i+1) = lambda - x(i)^2; % next point
  x(i+2) = x(i+1); % next point on diagonal
end
figure
plot(x(2:end-1),x(3:end),':') % web as dotted line
xlabel('x_n') % labels - increase font
ylabel('x_{n+1}')
axis([0 Xmax 0 Xmax]) % remove most ticks
axis square
hold on % keep on plotting
plot(x(2:end-1),x(3:end),'.','MarkerSize',10,'Color','k') %attempt putting dots
plot(Xall,lambda - Xall.^2,'LineWidth',2,'Color','k') % parabola
plot(Xall,Xall,'-.') %diagonal
lamFix = roots([1 1 -lambda]); % 2 fixed point
plot(max(lamFix),max(lamFix),'.','MarkerSize',20,'Color','k') %plot rightmost
return
end
