Image:Logistic-burification.png

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Logistic-burification.png‎ (568 × 393 pixels, file size: 60 KB, MIME type: image/png)

Burification diagram of a logistic map

Released by the author (User:Ap) into the public domain.

[edit] Generation scripts

Here are some GNU Octave scripts to experiment with the generation of bifurcation diagrams for the logistic map.

r_min = 2.5; r_max = 4; # the range of parameter values we study
n = 1000; # the number of parameter values we consider in this range

t_max = 1000; # how many iterations to simulate per parameter value
p_max = 100; # the last p_max iterations are plotted

x0 = 0.1; # we use the same initial value x0 for all parameters.

r = linspace(r_min, r_max, n);
pop = zeros(p_max, n);

for k = 1:n
  x = population(r(k), x0, t_max);
  pop(:, k) = x(t_max-p_max+1:t_max);
end

gset nokey;
plot(r, pop, 'b.');

function x =  population(r, x0, n)
# simulates n iterations of the logistic map with parameter
# r and initial value x0. The results are returned in the
# array x.
  x = zeros(n, 1);
  x(1) = x0;
  for k = 1:n-1
    x(k + 1) = r * x(k) * (1 - x(k));
  end

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