While loop inside another while loop

I'm trying to make a bifurcation map for the logistic model using while loops but it isn't working quite as I expected. The code is:

x = input('Initial condition');
rmin = input('Minimal r');
rmax = input('Maximal r');
h = input('Step size');
nf = input('Iteraction number');
k = input('Transient duration');
m = 1;
r = rmin;
while r <= rmax+h
  while m <= nf
    n = [0:m];
    x(m+1) = r*x(m)*(1-x(m));
    m = m+1;
  end
  R = r*ones(1, nf);
  hold on
  figure 1
  plot (R(k+1:nf), x(k+1:nf), '.')
  hold off
  r = r+h;
end

The inside while gives the x vector for the initial r, but won't update itself with the other r values generated by the external while loops. I end up with a plot, in wich all the r values have the same associated x like the following picture:

I shoud be getting a graphic like this:

Is there a way to make it with the while loops or something similar?

Answer 1

[Jan]

The main problem of your code is, that you increase m in the inner loop, but do not reset it to 1 inside the outer loop. So you append new x values, but you draw the same part x(k+1:nf) repeatedly. Move m = 1 inside the outer loop.

The editor warns already, that the line "n = [0:m];" is a waste of time only, because n is not used anywhere.

With the small changes and FOR loops for a simplification:

rmin = 2.8;
rmax = 4.0;
h    = 0.01;
nf   = 2e3;
k    = 1e3;
x0   = 0.5;

figure;  % Not figure(1): Integer figure numbers are outdated since 1999.
axes('NextPlot', 'add', ...  % same as: hold on
     'XLim', [rmin, rmax], 'YLim', [0, 1]);

x    = zeros(1, nf);   % Pre-allocate
x(1) = x0;             % Is not overwritten inside the loops! 
for r = rmin:h:rmax
   for m = 1:nf - 1
      x(m + 1) = r * x(m) * (1 - x(m));
   end
   plot(r, x(k+1:nf), 'r.');
   % plot(r, unique(round(x(k+1:nf), 6)), 'r.');   % Much faster!
   drawnow;
end

Answer 2

[Jan]

The code of my other questions spends the most time for updating the figure. Even closing the figure finally takes several seconds.

A version, which draws to a an array, which is displayed as image:

function Bifurcation
% x = input('Initial condition');
% rmin = input('Minimal r');
% rmax = input('Maximal r');
% h = input('Step size');
% nf = input('Iteraction number');
% k = input('Transient duration');

rmin  = 2.8;
rmax  = 4.0;
n     = 2e3;
trans = 1e3;
x0    = 0.5;

W     = 800;
WStep = (rmax - rmin) / W; 
H     = 500;
HLim  = [0, 1];
HVec  = linspace(HLim(1), HLim(2), H);

Img   = ones(H, W, 3);

FigH  = figure();
AxesH = axes(FigH, 'NextPlot', 'add', ...  % same as: hold on
             'XLim', [1, W], 'YLim', [1, H], ...
             'TickDir', 'out');
ImgH  = image(AxesH, Img);

x    = zeros(1, n);    % Pre-allocate
x(1) = x0;             % Is not overwritten inside the loops! 
for iW = 1:W
   r = rmin + (iW - 1) * WStep;
   for m = 1:n - 1
      x(m + 1) = r * x(m) * (1 - x(m));
   end
   
   % Slow graphics with different line objects:
   % plot(r, x(k+1:n), 'r.');
   % plot(r, unique(round(x(trans+1:n), 4)), 'r.');   % Much faster!
   
   q    = histc(x(trans:n), HVec);
   m    = (q ~= 0);
   maxq = max(q(m));
   Img(m, iW, :) = repmat(1 - (q(m) / maxq), [1, 1, 3]);
   ImgH.CData    = Img;
   drawnow;
end
end