#DidYouKnow: The #Collatz #Conjecture, also known as the "hailstone conjecture" or the "3n + 1 problem," is one of the most famous unsolved problems in mathematics.
The conjecture asks whether repeating two simple arithmetic operations will eventually transform every positive integer into 1
Collatz's Ant and Σ(n)
https://gbragafibra.github.io/2025/07/06/collatz_ant5.html
#HackerNews #Collatz #Ant #Collatz #Conjecture #Math #Blog #Σn
Collatz's Ant and Similarity of Landscapes
https://gbragafibra.github.io/2025/05/18/collatz_ant3.html
#HackerNews #Collatz #Ant #Similarity #Landscapes #Mathematics #Algorithm #Research
A shower thought turned into a beautiful Collatz visualization
https://abstractnonsense.com/collatz/
#HackerNews #showerthoughts #Collatz #visualization #abstractnonsense #creativity #techart
is anyone from mathstodon willing to critique this preprint? the author claims to have solved the Collatz conjecture and I have not found any holes in the proof yet.
https://www.preprints.org/manuscript/202502.2072/v3
The author first shows that collatz cycles have bounded growth, then proves the uniqueness of the 4-2-1 cycle. The ensuing claim is that this implies that all paths converge to 4-2-1.
It's all quite easy for me to follow, which raises my skepticism a bit.
#DidYouKnow: The #Collatz #Conjecture, also known as the "hailstone conjecture" or the "3n + 1 problem," is one of the most famous unsolved problems in mathematics.
The conjecture asks whether repeating two simple arithmetic operations will eventually transform every positive integer into 1
I algebraically expressed all possible combinations of the outcomes of #Collatz Conjecture with an iterative rule set to see how many I could prove as not producing x>0 as an integer (which would indicate a loop).
I have a tree with two sets of expressions that cannot loop. One for trivial reasons and one because the rules say you can't do that.
Anyone else want to play?
#Day11 of the #30DayChartChallenge, #MobileFriendly
🤔💭🔢 The Collatz Conjecture🤔
#rstats #dataviz #ggplot2 #Collatz #Conjecture #Distributions #visualisation #mobile
One day, one decomposition
A062060: Numbers with 10 odd integers in their Collatz (or 3x+1) trajectory
3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A062060.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A062060.html
#decompwlj #maths #mathematics #sequence #OEIS #javascript #php #3D #numbers #odd #integers #Collatz #trajectory #graph #threejs #webGL
Ich glaube, die #Collatz-Vermutung (auch "#Syracuse-Problem, dem #Ulam-Problem, der 3n + 1-Vermutung, vom #Hasse-Algorithmus oder dem #Kakutani-Problem.") ist nicht beweisbar, da die Funktionweise des #Algorithmus auf der axiomatischen Festlegung "gerader" und "ungerader" Zahlen beruht > nicht| ohne Rest durch 2 teilbar.
Doch was weiß ich schon?
Ich bin kein Mathematiker, nur ein Jurist, der den Gödelschen Unvollständigkeitssatz kennt.
One day, one decomposition
A061641: Pure numbers in the Collatz (3x+1) iteration. Also called pure hailstone numbers
3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A061641.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A061641.html
#decompwlj #maths #mathematics #sequence #OEIS #javascript #php #3D #pure #numbers #Collatz #iteration #hailstone #graph #threejs #webGL
@ColinTheMathmo Hi, You got overly excited about calling Chartodon when you were too busy Xmas Eve, but you needn't digest an entire conversation unless you want to.
My request was potentially simpler, and to quote my original post to you:
"It turns out that our new user Ben (Dec 12), who I was talking to a bit because we have a shared passion for factorization and related topics, is *also* interested in doing math related crafting and looming!
"I'm CC'ing you because I know there are a lot of people here who would be interested in such things, but I'm not sure how to put them in contact or if there's a list or something.
"Ben said '...I've also got an idea for a visualisation of the reverse #collatz conjecture in mod 6, 18, 54 etc but I want to do it as a craft project with coloured thread and I need to make a loom first.'
" https://mathstodon.xyz/@benpetersjones/111632982638466183
The original thread that you appeared to Chartodon:
@benpetersjones @ColinTheMathmo
"I think somewhere here is a visual proof of #collatz not looping."
Naturally that would be fantastic. Interesting lead / path you're following there.
@dougmerritt @ColinTheMathmo this is the Sharpie version of the reverse collatz conjecture. Very messy but I hope it makes some sense. My long-winded but too brief explanation may not help but all the non-4mod6 paths point in an upward direction. The 4mod6 numbers are either pink in a positive/upwards direction or black in a negative/downwards direction with an arrow. I think there's some merit in saying if a number grows to a higher number and onto a stable path/remainder like 0, 1, 2 or 3 then it must always grow to infinity. Also 2 out of the 3 4mod6 numbers also quickly get to a stable higher path. The only numbers still in doubt in my mind are the numbers like 17, 53, 161... that oscillate between 5 and 4mod6 for ages before inevitably moving to 3mod6 on a stable path. I think somewhere here is a visual proof of #collatz not looping.
@ColinTheMathmo It turns out that our new user Ben (Dec 12), who I was talking to a bit because we have a shared passion for factorization and related topics, is *also* interested in doing math related crafting and looming!
I'm CC'ing you because I know there are a lot of people here who would be interested in such things, but I'm not sure how to put them in contact or if there's a list or something.
Ben said "...I've also got an idea for a visualisation of the reverse #collatz conjecture in mod 6, 18, 54 etc but I want to do it as a craft project with coloured thread and I need to make a loom first."
@dougmerritt hi. I'm not really working on anything at the moment and I also feel like a bit of a fraud being here in the first place. Trying to get the lay of the land. The last thing I did was write some JS code to test the efficiency of my primality test. I've basically written the three sections but need to join them up. That's essentially a trial division module that outputs remainders which feeds into a module that sieves out impossible square numbers and the trial division also reduces the upper bound for square numbers. There's also a brute force calculation based on the remaining square numbers and a bunch of arrays.
I've also got an idea for a visualisation of the reverse #collatz conjecture in mod 6, 18, 54 etc but I want to do it as a craft project with coloured thread and I need to make a loom first.
Plus Christmas and surfing etc.
The Collatz conjecture drawn as Bezier curves in a chaotic rainbow.
Available for minting on https://fxhash.xyz/generative/25615
As always there's royalties to the minters, @GirlsWhoCode and @ProcessingOrg
#generativeart #p5js #collatz #javascript #tezos #fxhash #nft
[Matt Parker] on the completion of The Great Collatz Collab in which hundreds of schools picked 3 digit numbers to test the Collatz Conjecture, which were then collated into a single large map
https://youtu.be/lnpFqdQJAFA
The project resources including downloadable map:
https://think-maths.co.uk/collatz-collab
#youtube #CollatzConjecture #Collatz #maths #mathematics #STEM #mathstodon #mastomaths #math
🧮 A new algorithm to multiply two numbers, out of nowhere. Extremely simple!
It's basically a simple double iteration of a function of the 3n+1 problem (Collatz conjecture).
"#Multiplication #Algorithm Based on #Collatz Function" (David #Barina, 15 mai 2020)
• https://link.springer.com/article/10.1007%2Fs00224-020-09986-5
• https://sci-hub.uno/10.1007/s00224-020-09986-5
It is conditioned on Collatz conjecture being true. Which seems to be the case, although we can't prove it. (But one must always be wary of this kind of belief.)
