Dror Bar-Natan: Classes: 2002-03: Math 157 - Analysis I: | (235) |
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i did it in FORTRAN. it's very small and simple.Here's his program:i basically put the computed points in a file (in columns delimited by a space) and plotted them in Maple (but i supposed that you can use whatever program that you like). there are a lot of points though as my partition of [0,1] is quite fine (N = 2000). you can change this if you like, but it makes a nice picture.
And here are his graphs:program Chaos implicit none ! -----------------------------------------------Declare real*8 c, f_c, h integer*4 N, counter parameter (N = 2000) ! -----------------------------------------------Initialize h = 1./N c = 0. open(unit = 10, file = 'chaos') ! -----------------------------------------------Compute do while (.true.) if (c .gt. 1.) then exit end if f_c = .5 ! ----------------- Throw out a few 'generations' to get to the asymptotic behaviour do counter = 1, 125 f_c = 4*c*(f_c - f_c*f_c) end do ! ---------------- Let's keep these points and write them to our file do counter = 1, 75 f_c = 4*c*(f_c - f_c*f_c) write(10,*) c, f_c end do c = c + h end do close(10) end