from pylab import *
from numpy import NaN
from matplotlib.colors import LogNorm
dr, dx = .001, .001
max_it = 1000000
R = arange(2.4, 4, dr)
X = arange(0, 1, dx)
Z = zeros((len(X), len(R)))
for ir, r in enumerate(R):
print (ir, "of", len(R))
z = .25
for i in range(1000):
z = r * z * (1 - z)
for i in range(max_it):
z = r * z * (1 - z)
Z[-int(z / dx), ir] += 1
Z[:, ir] *= count_nonzero(Z[:, ir])
Z = where(Z > 0, Z, NaN)
save("logmap", Z) # save array to file
# pick color bar range:
zmi = .005 * nanmax(Z)
zma = .1 * nanmax(Z)
imshow(Z, cmap = plt.cm.viridis_r, vmin = zmi, vmax = zma,
interpolation = 'none', norm = LogNorm(),
extent = (R.min(), R.max(), X.min(), X.max()))
xlabel("r")
ylabel("x")
savefig("Logistic Map Bifurcation Diagram, Matplotlib.svg")
show()
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