Collatz Conjecture by autolisp

June 17, 2022

this is a simple routine to put in numbers into the Collatz conjecture.

https://en.wikipedia.org/wiki/Collatz_conjecture

Command

- collatz : graphic mode, like the gif above.

- collatztxt : text mode, like below

Command: COLLATZTXT
 input start number : 12302198909
 12302198909>36906596728>18453298364>9226649182>4613324591>13839973774>6919986887>20759960662>10379980331>31139940994>15569970497>46709911492>23354955746>11677477873>35032433620>17516216810>8758108405>26274325216>13137162608>6568581304>3284290652>1642145326>821072663>2463217990>1231608995>3694826986>1847413493>5542240480>2771120240>1385560120>692780060>346390030>173195015>519585046>259792523>779377570>389688785>1169066356>584533178>292266589>876799768>438399884>219199942>109599971>328799914>164399957>493199872>246599936>123299968>61649984>30824992>15412496>7706248>3853124>1926562>963281>2889844>1444922>722461>2167384>1083692>541846>270923>812770>406385>1219156>609578>304789>914368>457184>228592>114296>57148>28574>14287>42862>21431>64294>32147>96442>48221>144664>72332>36166>18083>54250>27125>81376>40688>20344>10172>5086>2543>7630>3815>11446>5723>17170>8585>25756>12878>6439>19318>9659>28978>14489>43468>21734>10867>32602>16301>48904>24452>12226>6113>18340>9170>4585>13756>6878>3439>10318>5159>15478>7739>23218>11609>34828>17414>8707>26122>13061>39184>19592>9796>4898>2449>7348>3674>1837>5512>2756>1378>689>2068>1034>517>1552>776>388>194>97>292>146>73>220>110>55>166>83>250>125>376>188>94>47>142>71>214>107>322>161>484>242>121>364>182>91>274>137>412>206>103>310>155>466>233>700>350>175>526>263>790>395>1186>593>1780>890>445>1336>668>334>167>502>251>754>377>1132>566>283>850>425>1276>638>319>958>479>1438>719>2158>1079>3238>1619>4858>2429>7288>3644>1822>911>2734>1367>4102>2051>6154>3077>9232>4616>2308>1154>577>1732>866>433>1300>650>325>976>488>244>122>61>184>92>46>23>70>35>106>53>160>80>40>20>10>5>16>8>4>2>1

code is below

; COLLATZ - 2022.06.17 exceed
; this is a simple routine to plug in numbers into the "Collatz conjecture"
;
; Command List
; collatztxt - Only text output. When you enter a number, it does a Colatz conjecture until it reaches 1.
; collatz - run collatz guesses by 100, starting at 2 It rotates +5 degrees for odd numbers and -5 degrees for even numbers.
; It asks if you want to continue every 100 in case of freezing.

(defun c:collatz ( / a )
  (setq a 1)
  (while (getstring "\n continue? (SpaceBar - Continue / ESC - End) - ")
    (repeat 100
      (ex:collatzgr a)
      (setq a (+ a 1))
    )
    (princ "\n collatz graph done - from ")
    (princ (- a 100))
    (princ " to ")
    (princ a)
    (command "_.Zoom" "_E")
  )
  (princ)
)

(defun c:collatztxt ( / n )
  (setq n (getreal "\n input start number : "))
  (princ (strcat "\n " (rtos n 2 0)))
  (while (> n 1)
    (cond 
      ((= (rem n 2) 1)
        (setq n (+ (* n 3) 1))
        (princ (strcat ">" (rtos n 2 0)))
      )
      ((= (rem n 2) 0)
        (setq n (/ n 2))
        (princ (strcat ">" (rtos n 2 0)))
      )
    )
  )
  (princ)
)


(defun EX:COLLATZGR ( n / mspace basedeg deltadeg basept pt2 collatzline ) 
  (vl-load-com)
  (defun dtr (x) (* pi (/ x 180.0)) )
  (defun rtd (x) (* x (/ 180.0 pi)) )
  (setq mspace (vla-get-modelspace (vla-get-activedocument (vlax-get-acad-object))))

  (setq basedeg 90)
  (setq deltadeg 5)
  (setq basept (list 0 0 0))

  ;(princ (strcat "\n " (rtos n 2 0)))
  (while (> n 1)
    (cond 
      ((= (rem n 2) 1)
        (setq n (+ (* n 3) 1))
        (setq pt2 (polar basept (dtr basedeg) n))
        (setq basedeg (+ basedeg deltadeg))
        (setq collatzline (vla-addline mspace (vlax-3d-point basept)(vlax-3d-point pt2)))
        (setq basept pt2)
        ;(princ (strcat ">" (rtos n 2 0)))
      )
      ((= (rem n 2) 0)
        (setq n (/ n 2))
        (setq pt2 (polar basept (dtr basedeg) n))
        (setq basedeg (- basedeg deltadeg))
        (setq collatzline (vla-addline mspace (vlax-3d-point basept)(vlax-3d-point pt2)))
        (setq basept pt2)
        ;(princ (strcat ">" (rtos n 2 0)))
      )
    )
  )
  (princ)
)