PROGRAM iterate_map               ! iterate logistic map
CALL set_up_windows(#1,#2)
DO
   CALL initial(x,r,#1,#2,flag$)
   CALL map(x,r,#1,#2,flag$)
LOOP until flag$ = "stop"
END

SUB initial(x0,r,#1,#2,flag$)
    WINDOW #2
    INPUT prompt "growth parameter (0 < r <= 1) = ": r
    LET x0 = 0.3
    CLEAR
    BOX LINES 0,1000,0,1
    SET CURSOR 1,2
    PRINT "r ="; r
    LET flag$ = ""
END SUB

SUB set_up_windows(#1,#2)
    OPEN #1: screen 0,1,0,0.5     ! text
    OPEN #2: screen 0,1,0.5,1     ! graphics
    LET nmax = 1000
    LET margin = 0.01*nmax
    SET WINDOW -margin,nmax+margin,-0.01,1.01
END SUB

SUB map(x,r,#1,#2,flag$)
    LET iterations = 0
    DO
       LET x = 4*r*x*(1 - x)      ! iterate map
       LET iterations = iterations + 1      ! number of iterations
       WINDOW #1
       SET COLOR "black/white"
       PRINT USING "#.######": x;
       ! period doubling implies convenient to start new line
       ! every 2^n iterations, where n = 2 or 3.
       IF mod(iterations,8) = 0 then PRINT  ! new line
       WINDOW #2
       SET COLOR "red"
       PLOT iterations,x
       IF key input then CALL change(#1,#2,flag$)
    LOOP until flag$ = "stop" or flag$ = "change"
    WINDOW #1
    PRINT
    PRINT "number of iterations = "; iterations
END SUB

SUB change(#1,#2,flag$)
    GET KEY k
    IF (k = ord("c")) or (k = ord("C")) then
       LET flag$ = "change"
       SET COLOR "black/white"
    ELSE IF (k = ord("s")) or (k = ord("S")) then
       LET flag$ = "stop"
    END IF
END SUB