benford.lisp

;; pseudo-random numbers don't follows Benford's Law.

(ql:quickload :cl-spark)


(defun random-numbers (max count)
  (loop repeat count
        for n := (random max)
        when (plusp n)
          collect n))

(defun most-significant-digit (x)
  (nth-value 0 (floor (/ x (expt 10 (floor (log x 10)))))))

(defun histogram (numbers)
  (loop with hist := (make-array 9 :initial-element 0)
        for x in numbers
        do (incf (aref hist (1- x)))
        finally (return hist)))

(defun main (&optional (max 1000000) (count 1000000))
  (let* ((numbers (random-numbers max count))
         (digits (mapcar #'most-significant-digit numbers))
         (hist (histogram digits)))
      (spark:spark (coerce hist 'list))))

#|
CL-USER> (main)
"▅▇▇▆▄▁▄█▄"
CL-USER> (main)
"▆▅▂▁▆▁▂▁█"
CL-USER> (main)
"▄▁█▁▃▅▄▄▂"
CL-USER> (main)
"▃▅▂▁▁█▂▃▂"
CL-USER> (main)
"▁▆▅█▄▂▆▅▅"
CL-USER> (main)
"▂▃▅█▂▁▃▂▂"
CL-USER> (main)
"▅▅▃▁▂█▅▃▁"
CL-USER> (main)
"█▆▅▃▇▃▃▃▁"
CL-USER> (main)
"▂▇▇█▇▃▇▃▁"
CL-USER> (main)
"▇▇▂▁▄▇▄█▆"
CL-USER> (main)
"▆▁▄▂▃█▆▆▇"
CL-USER> (main)
"▁▁▆▂▃▂▃█▇"
CL-USER> (main)
"▂▄▄█▁▆▂▄▆"
CL-USER> (main)
"▅▄▇▅▄█▁▃▂"
CL-USER> (main)
"▁▅▄▃▃▄▂▄█"
CL-USER> (main)
"▃▅▂▃█▅▁▃▆"
|#