File:Logistic Map Bifurcation Diagram, Matplotlib, zoomed.png

from pylab import *
from numpy import NaN
from matplotlib.colors import LogNorm
import time
from sys import getsizeof

dr, dx = .001/4, .001/4

# Perform max_it iterations at a time, repeated over it_cyc cycles.
# (This is done so that the memory requirement for the out array
# does not get too big. Lower max_it if you do not have enough free RAM.)
max_it = 10000
it_cyc = 10

R = arange(3.5, 4, dr)
X = arange(0, 1, dx)
Z = zeros((len(X), len(R)))

z = zeros((len(R)))
out = zeros((max_it, len(R)))
print("out array size is", int(getsizeof(out) / 1024 / 1024), "MB")

start = time.time()

for cy in range(it_cyc):
	z[:] = (cy + .5) / it_cyc	# use different starting values, not just 0.25
	for i in range(1000):
		z[:] = R[:] * z[:] * (1 - z[:])

	print("cycle", cy + 1, "of", it_cyc)
	for i in range(max_it):
		if i and not i % 1000:
			itpers = i / (time.time() - start)
			left = (max_it - i) / itpers
			#print (i, ",", int(left), "s left for iterations")
		z[:] = R[:] * z[:] * (1 - z[:])
		out[i, :] = z[:]

	for ir, r in enumerate(R):
		#print (ir, "of", len(R), "histograms done")
		h = histogram(out[:, ir], bins = list(X))[0]
		Z[1:, ir] += h[::-1]

for ir, r in enumerate(R):
	Z[:, ir] *= count_nonzero(Z[:, ir])

Z = where(Z > 0, Z, NaN)
save("logmap", Z)	# save array to file

# pick color bar range:
zmi = .001 * nanmax(Z)
zma = .1   * nanmax(Z)

imshow(Z, cmap = plt.cm.viridis_r, vmin = zmi, vmax = zma,
  interpolation = 'none', norm = LogNorm(), aspect = "auto",
  extent = (R.min(), R.max(), X.min(), X.max()))
xlabel("r")
ylabel("x")
axis((3.5, 4, 0, 1))
# SVG size is 12 MB and crashes Firefox, so save as PNG instead:
savefig("Logistic Map Bifurcation Diagram, Matplotlib, zoomed.png", dpi = 600)
print("===", max_it * it_cyc, "total iterations")
print("===", int(time.time() - start), "s total time")
show()