# logmap.py

A Python program to compute a plot of the logistic map invariant measures.

logmap.py — Python Source, 0Kb

## File contents

# This program will compute the iterates of the logistic map, and histogram # them in a two-dimensional (r,x) grid. # can choose to plot on screen or save as a png. from pylab import * screen = True # The size of the grid in the R and X dimensions, and the range of r RDIM = 1000 XDIM = 1000 rmin = 3.0 rmax = 4.0 # Get started. Initialize histogram h = zeros((RDIM,XDIM)) # Will compute all values of r in parallel. So we will have RDIM copies of x, r x=rand(RDIM) # might want to start from the maximum 0.5, or from random r= rmin+(rmax-rmin)*arange(RDIM)/(RDIM-1) in0 = range(RDIM) # iterate until the transients decay. for i in range(10000): x=r*x*(1.0-x) # iterate and histogram for i in range(5000): x=r*x*(1.0-x) ind = floor( x*(XDIM-1) ).astype(int) h[in0,ind] += 1 # plot according to choice above. if( screen ): imshow(log(h[:,::-1].T+1),aspect='auto',extent=(rmin,rmax,0.0,1.0)) show() else: imsave("logmap.png",log(h.T+1),cmap=cm.jet,origin='lower')