Talk:710: Collatz Conjecture - Revision history

Boochin at 16:04, 26 March 2024

2024-03-26T16:04:46Z

Boochin at 16:04, 26 March 2024

2024-03-26T16:04:08Z

198.41.238.106 at 01:31, 28 July 2021

2021-07-28T01:31:28Z

198.41.238.108 at 01:29, 28 July 2021

2021-07-28T01:29:59Z

198.41.238.109 at 01:29, 28 July 2021

2021-07-28T01:29:40Z

198.41.238.108 at 01:28, 28 July 2021

2021-07-28T01:28:25Z

198.41.238.108 at 01:26, 28 July 2021

2021-07-28T01:26:21Z

MigB at 11:41, 13 April 2021

2021-04-13T11:41:55Z

172.68.59.84 at 13:40, 22 November 2018

2018-11-22T13:40:53Z

International Space Station at 09:36, 25 January 2016

2016-01-25T09:36:05Z

@@ Line 76: / Line 76: @@
   import matplotlib.pyplot as plt
   start_number = int(input("Enter a number:\n"))
   loop_count = 0
   full_list = [start_number]
   while start_number != 1:
     loop_count += 1
@@ Line 93: / Line 91: @@
     else:
       print("Error")
   print("Iterations: " + str(loop_count))
   plt.plot(full_list)
   plt.title('Graph (Linear)')
   plt.xlabel('Steps')
   plt.ylabel('Hight')
   plt.show()

← Older revision		Revision as of 16:04, 26 March 2024
Line 72:		Line 72:

	--[[Special:Contributions/198.41.238.106\|198.41.238.106]] 01:31, 28 July 2021 (UTC)		--[[Special:Contributions/198.41.238.106\|198.41.238.106]] 01:31, 28 July 2021 (UTC)
		+
		+	:If we're sharing code, I made a Python script that calculates a string for any given number and then graphs it:
		+
		+	import matplotlib.pyplot as plt
		+
		+	start_number = int(input("Enter a number:\n"))
		+	loop_count = 0
		+	full_list = [start_number]
		+
		+	while start_number != 1:
		+	loop_count += 1
		+	if start_number % 2 == 0:
		+	start_number = int(start_number / 2)
		+	print(start_number)
		+	full_list.append(start_number)
		+	elif start_number % 2 == 1:
		+	start_number = int(start_number * 3 + 1)
		+	print(start_number)
		+	full_list.append(start_number)
		+	else:
		+	print("Error")
		+
		+	print("Iterations: " + str(loop_count))
		+	plt.plot(full_list)
		+
		+	plt.title('Graph (Linear)')
		+	plt.xlabel('Steps')
		+	plt.ylabel('Hight')
		+
		+	plt.show()

@@ Line 47: / Line 47: @@
 I wrote a program to calculate the tree (Python 3.9), but you have to install treelib. Do this by typing 'pip install treelib' in the terminal. The program:
-    from treelib import *
+ from treelib import *
-    tree=Tree()
+ tree=Tree()
-    levels=int(input('Levels of tree? '))
+ levels=int(input('Levels of tree? '))
-    start=int(input('Starting number? '))
+ start=int(input('Starting number? '))
-    tree.create_node(start, start)
+ tree.create_node(start, start)
-    def f(x):
+ def f(x):
-        global tree
+     global tree
-        if tree.depth(x)==tree.depth():
+     if tree.depth(x)==tree.depth():
-            return True
+         return True
-        else:
+     else:
-            return False
+         return False
-    def collatz(x):
+ def collatz(x):
-        if x%2==0 and x%3==1 and x!=4:
+     if x%2==0 and x%3==1 and x!=4:
-            return [(x-1)//3,x*2]
+         return [(x-1)//3,x*2]
-        else:
+     else:
-            return [x*2]
+         return [x*2]
-    for i in range(levels):
+ for i in range(levels):
-        N = list(tree.filter_nodes(f))
+     N = list(tree.filter_nodes(f))
-        for i in N:
+     for i in N:
-            c=collatz(i.tag)
+         c=collatz(i.tag)
-            for j in c:
+         for j in c:
-                tree.create_node(j,j,i)
+             tree.create_node(j,j,i)
-    tree.show(line_type='ascii')
+ tree.show(line_type='ascii-ex')
---[[Special:Contributions/198.41.238.108|198.41.238.108]] 01:29, 28 July 2021 (UTC)

@@ Line 70: / Line 70: @@
                  tree.create_node(j,j,i)
      tree.show(line_type='ascii')
- --[[Special:Contributions/198.41.238.109|198.41.238.109]] 01:29, 28 July 2021 (UTC)
+--[[Special:Contributions/198.41.238.108|198.41.238.108]] 01:29, 28 July 2021 (UTC)

@@ Line 48: / Line 48: @@
      from treelib import *
-tree=Tree()
+    tree=Tree()
-levels=int(input('Levels of tree? '))
+    levels=int(input('Levels of tree? '))
-start=int(input('Starting number? '))
+    start=int(input('Starting number? '))
-tree.create_node(start, start)
+    tree.create_node(start, start)
-def f(x):
+    def f(x):
-    global tree
+        global tree
-    if tree.depth(x)==tree.depth():
+        if tree.depth(x)==tree.depth():
-        return True
+            return True
-    else:
+        else:
-        return False
+            return False
-def collatz(x):
+    def collatz(x):
-    if x%2==0 and x%3==1 and x!=4:
+        if x%2==0 and x%3==1 and x!=4:
-        return [(x-1)//3,x*2]
+            return [(x-1)//3,x*2]
-    else:
+        else:
-        return [x*2]
+            return [x*2]
-for i in range(levels):
+    for i in range(levels):
-    N = list(tree.filter_nodes(f))
+        N = list(tree.filter_nodes(f))
-    for i in N:
+        for i in N:
-        c=collatz(i.tag)
+            c=collatz(i.tag)
-        for j in c:
+            for j in c:
-            tree.create_node(j,j,i)
+                tree.create_node(j,j,i)
-tree.show(line_type='ascii') --[[Special:Contributions/198.41.238.108|198.41.238.108]] 01:28, 28 July 2021 (UTC)
+    tree.show(line_type='ascii')

← Older revision		Revision as of 01:26, 28 July 2021
Line 44:		Line 44:
	33: 1		33: 1
	[[User:International Space Station\|International Space Station]] ([[User talk:International Space Station\|talk]]) 09:36, 25 January 2016 (UTC)		[[User:International Space Station\|International Space Station]] ([[User talk:International Space Station\|talk]]) 09:36, 25 January 2016 (UTC)
		+
		+	I wrote a program to calculate the tree (Python 3.9), but you have to install treelib. Do this by typing 'pip install treelib' in the terminal. The program:
		+
		+	from treelib import *
		+	tree=Tree()
		+	levels=int(input('Levels of tree? '))
		+	start=int(input('Starting number? '))
		+	tree.create_node(start, start)
		+	def f(x):
		+	global tree
		+	if tree.depth(x)==tree.depth():
		+	return True
		+	else:
		+	return False
		+	def collatz(x):
		+	if x%2==0 and x%3==1 and x!=4:
		+	return [(x-1)//3,x*2]
		+	else:
		+	return [x*2]
		+	for i in range(levels):
		+	N = list(tree.filter_nodes(f))
		+	for i in N:
		+	c=collatz(i.tag)
		+	for j in c:
		+	tree.create_node(j,j,i)
		+	tree.show(line_type='ascii')

@@ Line 5: / Line 5: @@
 ::: It's pretty obvious the person you replied to has a head for mathematics. If you really think this is at all similar to the Goatee Guy from [[675: Revolutionary]], then you are sorely mistaken. [[Special:Contributions/172.68.59.84|172.68.59.84]] 13:40, 22 November 2018 (UTC)
 :: It seems way too general to be much more than "asked," and I am sure that it has been addressed in its simpler forms. In any case, there is enough amateur, recreational, and serious mathematical literature on it to find out that there are indeed two failure cases: a starting Collatz number results in an infinitely increasing sequence, or a loop exists apart from the 4-2-1 loop. (Curiously enough, some loops exist when negative numbers are allowed.) Stuff like this and Goldbach made me realize just how hard simple things can get. --[[User:Quicksilver|Quicksilver]] ([[User talk:Quicksilver|talk]]) 03:04, 20 August 2013 (UTC)
+:: A way to ask if the trajectory eventually reach 1 is to ask if the number is increasing or decreasing. If it is decreasing, it will eventually his a number already confirmed earlier to be on the trajectory. Whenever (n*3 + 1) is applied, the result is always even, and must be divided by two. But (n*3 + 1) / 2 > n. So the value will increase unless it hit a positive value more often than every other time. If it hit even 2 out of 3 times, the value decrease as (n*3 + 1) / (2*2) < n for all values of n > 1.
 Just for fun, here's 710's Collatz Trajectory.

@@ Line 3: / Line 3: @@
 :And (again without checking the Wiki link), I suppose the conjecture could fail in one of two cases.  Firstly if multiplying by three and adding one would take us to another odd number.  Which cannot happen, because (odd*3) will be odd, so (odd*3)+1 is even.  Which leads us to the possibility that the even number leads back to a prior odd number, to circle around again.  There's no trivial case of (n*3)+1 => m, (m/2) => n, although there is the case of (n*3)+1 => m, (m/2) => o, (o/2) => n, for n=1.  How, though, could we evaluate f<sub>1|2</sub>(x<sub>i</sub>) => x<sub>i+1</sub> for all countably finite limits to i, given the rules of which f() function to use, to ensure that x<sub>i</sub> never equals x<sub>0</sub>.  Now, ''that's'' a question and a half. Which I suspect has already been asked. And a half. [[Special:Contributions/31.111.50.225|31.111.50.225]] 21:36, 7 May 2013 (UTC)
 :: Wonderful! "Without checking the wiki link"... The guy from [[675: Revolutionary]] in real life![[User:Mumiemonstret|Mumiemonstret]] ([[User talk:Mumiemonstret|talk]]) 15:14, 17 October 2014 (UTC)
+::: It's pretty obvious the person you replied to has a head for mathematics. If you really think this is at all similar to the Goatee Guy from [[675: Revolutionary]], then you are sorely mistaken. [[Special:Contributions/172.68.59.84|172.68.59.84]] 13:40, 22 November 2018 (UTC)
 :: It seems way too general to be much more than "asked," and I am sure that it has been addressed in its simpler forms. In any case, there is enough amateur, recreational, and serious mathematical literature on it to find out that there are indeed two failure cases: a starting Collatz number results in an infinitely increasing sequence, or a loop exists apart from the 4-2-1 loop. (Curiously enough, some loops exist when negative numbers are allowed.) Stuff like this and Goldbach made me realize just how hard simple things can get. --[[User:Quicksilver|Quicksilver]] ([[User talk:Quicksilver|talk]]) 03:04, 20 August 2013 (UTC)

← Older revision		Revision as of 09:36, 25 January 2016
Line 5:		Line 5:

	:: It seems way too general to be much more than "asked," and I am sure that it has been addressed in its simpler forms. In any case, there is enough amateur, recreational, and serious mathematical literature on it to find out that there are indeed two failure cases: a starting Collatz number results in an infinitely increasing sequence, or a loop exists apart from the 4-2-1 loop. (Curiously enough, some loops exist when negative numbers are allowed.) Stuff like this and Goldbach made me realize just how hard simple things can get. --[[User:Quicksilver\|Quicksilver]] ([[User talk:Quicksilver\|talk]]) 03:04, 20 August 2013 (UTC)		:: It seems way too general to be much more than "asked," and I am sure that it has been addressed in its simpler forms. In any case, there is enough amateur, recreational, and serious mathematical literature on it to find out that there are indeed two failure cases: a starting Collatz number results in an infinitely increasing sequence, or a loop exists apart from the 4-2-1 loop. (Curiously enough, some loops exist when negative numbers are allowed.) Stuff like this and Goldbach made me realize just how hard simple things can get. --[[User:Quicksilver\|Quicksilver]] ([[User talk:Quicksilver\|talk]]) 03:04, 20 August 2013 (UTC)
		+
		+
		+	Just for fun, here's 710's Collatz Trajectory.
		+	0: 710
		+	1: 355
		+	2: 1066
		+	3: 533
		+	4: 1600
		+	5: 800
		+	6: 400
		+	7: 200
		+	8: 100
		+	9: 50
		+	10: 25
		+	11: 76
		+	12: 38
		+	13: 19
		+	14: 58
		+	15: 29
		+	16: 88
		+	17: 44
		+	18: 22
		+	19: 11
		+	20: 34
		+	21: 17
		+	22: 52
		+	23: 26
		+	24: 13
		+	25: 40
		+	26: 20
		+	27: 10
		+	28: 5
		+	29: 16
		+	30: 8
		+	31: 4
		+	32: 2
		+	33: 1
		+	[[User:International Space Station\|International Space Station]] ([[User talk:International Space Station\|talk]]) 09:36, 25 January 2016 (UTC)