program bifurcation
      implicit none
      real r,x_ini,x,xi
      integer pgopen,i,i_again,isymbol,n_gen,j,n_group_size

      isymbol = -1

      write (*,*) 'This plots fix-points x* of x_n+1=4rx_n(1-x_n+1).'
      write (*,*)
c     write (*,*) 'What is the initial value of x (0 < x < 1) ?'
c     read (*,*) x_ini
      x_ini = 0.5

      if ( pgopen('/xwin') .le. 0 ) stop
c     call pgpap(5.0,0.75)

 100  write (*,*) 'What is the numer of generation for the mapping ?'
      read (*,*) n_gen

      call pgeras
      call pgsci(1)
      call pgenv(0.0, 1.0, 0.0, 1.0, 0, 0)
      call pglab('r','x','x\u*')

      n_ group_size = n_gen/15

      do j=1,1000
      r = j/1000.0
      x = x_ini
        do i=1,n_gen
          x = 4*r*x*(1-x)
          call pgsci(i/n_group_size)
c         if (i.gt.(0.1*n_gen)) call pgpt(1,r,x,isymbol)
          call pgpt(1,r,x,isymbol)
        end do
      end do

 102  write (*,*) 'Again ? (1=YES;0=NO)'
      read (*,*) i_again
      if (i_again.eq.1) goto 100
      if (i_again.eq.0) stop
      goto 102

      end