PROGRAM graph_sol
! graphical solution for trajectory of logistic map
CALL initial(x,r,iterate)
CALL draw_function(r,iterate)
CALL trajectory(x,r,iterate)      ! press any key to stop
END

SUB initial(x0,r,iterate)
    INPUT prompt "control parameter r = ": r
    INPUT prompt "initial value of x = ": x0
    INPUT prompt "iterate of f(x) = ": iterate
    CLEAR
    PRINT "r ="; r
END SUB

SUB draw_function(r,iterate)
    DECLARE DEF f
    LET nplot = 200          ! # of points at which function computed
    LET delta = 1/nplot
    LET margin = 0.1
    SET WINDOW -margin,1 + margin,-margin,1 + margin
    PLOT LINES: 0,0;1,1      ! draw diagonal line y = x
    PLOT LINES: 0,1;0,0;1,0  ! draw axes
    PLOT                     ! lift pen
    SET COLOR "red"
    LET x = 0
    FOR i = 0 to nplot
        LET y = f(x,r,iterate)
        PLOT x,y;
        LET x = x + delta
    NEXT i
END SUB

SUB trajectory(x,r,iterate)
    DECLARE DEF f
    LET y0 = 0
    LET x0 = x
    SET COLOR "blue"
    DO
       LET y = f(x,r,iterate)
       PLOT LINES: x0,y0; x0,y; y,y
       LET x0 = y
       LET y0 = y
       LET x = y
    LOOP until key input
    GET KEY k
END SUB

DEF f(x,r,iterate)           ! f defined by recursive procedure
    IF iterate > 1 then
       LET y = f(x,r,iterate - 1)
       LET f = 4*r*y*(1 - y)
    ELSE
       LET f = 4*r*x*(1 - x)
    END IF
END DEF