Image:Logistic-burification.png
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Burification diagram of a logistic map
Released by the author (User:Ap) into the public domain.
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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