Collatz Prime Ratio Visualizer

CollatzPrimeRatio.lisp

(defmacro while (test &body body)
  `(do ()
       ((not ,test))
     ,@body))

(defmacro with-gensyms (syms &body body)
  `(let ,(mapcar #'(lambda (x) `(,x (gensym))) syms)
     ,@body))

(defmacro collect-list (end-condition next-value var)
  "Generates a list based on the next-value provided."
  (with-gensyms (acc)
    `(let ((,acc nil))
       (while (not ,end-condition)
	 (push ,var ,acc)
	 (setq ,var ,next-value))
       (nreverse (cons ,var ,acc)))))

(defun collatz (start)
  (collect-list (= start 1)
		(if (evenp start)
		    (/ start 2)
		    (+ 1 (* 3 start)))
		start))

(defun fn-ratio (x fn eqc)
  (labels ((rec (y e acc)
	     (if (> y x)
		 (reverse acc)
		 (rec
		  (+ y 1)
		  (if (funcall eqc (funcall fn y))
		      (incf e)
		      e)
		  (cons (float (/ e y))
			acc)))))
    (rec 1 0 nil)))

(defun primep (x &optional (p 2))
  (cond ((< x 2) nil)
	((= x 2) t)
	((= 0 (rem x p)) nil)
	((>= p (sqrt x)) t)
	(t (primep x (+ p 1)))))

(with-open-file (s "data.txt" :direction :output :if-exists :overwrite)
	   (dolist (x (fn-ratio 5000000 #'(lambda (x) (length (collatz x))) #'primep))
		(format s "~a~%" x))

VisulaizeDataTxt.py

import matplotlib.pyplot as plt
from mpl_toolkits.axes_grid.axislines import SubplotZero
file = open("data.txt","rU")
xs = []
for line in file:
    xs.append(float(line.strip()))
len(xs)
fig = plt.figure(1)
ax = SubplotZero(fig,111,
        xlabel="N",
        ylabel="Number of Prime Lengthed Chains Less Than or Equal To N Divided By N")
fig.add_subplot(ax)
x = range(1,len(xs)+1)
ax.plot(x,xs)
plt.show()