Dror Bar-Natan: Classes: 2002-03: Math 157 - Analysis I: (235) Next: Class Notes for the Week of March 3 (1 of 6) Previous: Wang Ying's Solution of Homework Assignment 21

# HW21: Solution of Just for Fun Problem

Norm Townsend wrote:
i did it in FORTRAN. it's very small and simple.

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.

Here's his program:
```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
```
And here are his graphs: