Plotting the bifurcation diagram for the logistic equation.

logistic_equation_4.rkt

;;; Plots the bifurcation diagram, using the given starting point
;;; x-init (using 100 iterations, and plots the values for the
;;; last 30.)
(define (plot-bifurcation-diagram x-init)
  (define (steady-state-points)
    (let ((points '())
          (step-size 0.001)
          (iterations 100)
          (keep-last-points 30))
      (for ((r (in-range 0 4 step-size)))
        (let ((xs (list x-init)))
          (for ((n (in-range 2 iterations)))
            (let ((x (car xs)))
              (set! xs (cons (logistic-equation r x) xs))))
          (set! points 
                (append points (map (lambda (x) (vector r x)) 
                                    (take xs keep-last-points))))))
      points))
  (parameterize ((plot-width 400)
                 (plot-height 400)
                 (plot-font-size 11)
                 (plot-x-label "r")
                 (plot-y-label "x"))
    (plot (points (steady-state-points) 
                  #:x-min 0 #:x-max 4 #:y-min 0 #:y-max 1
                  #:sym 'dot #:color 'blue))))