15:24/15:27 - suffice it to say this inspired me to have a fun little jaunt with some ruby code for generating a graphviz "dot" (or "twopi"; I played with both) file, and exploring what the directed graph could look like... with different colors based on size of number, even/odd status, and even for primes. Fun times! Thanks!
If I understand her @9:42 correctly, that is 2228 numbers for a super map with all 900 3-digit numbers. Would there be any 2- or 1- digit numbers missing from that super map? If "yes", which ones would be missing? If "no", how many 3-digit numbers do you have to add to the super map (starting at 100 and going in numeric order) in order to have used all the numbers < 100?
I am not 100% sure if there is all 2 digit numbers in the map, but I know that if you just multibly 2-digit numbers you will get every 2 digit number that way before 200, because biggest one is 99*2 =198 and second biggest are 98*2 or 49*2*2 = 196. but is there way to get 99 before 198 if you start in order... No. if you could, then you should be able to get it by from odd number that you would multible 3 times and add 1, but you can try that in reverse to 199 (199-1)/3 is not whole number, nor (199*2-1)/3, nor (199*2*2-1)/3 etc. there is always that 2/3 left over there. so you need to go in order from 100 to 198, then you get every 2-digit number :) (there is lot of useless numbers in between and I don't know what would be bethween [X-198] or shortest order around that 198 number, but probably lot shorter than 99 numbers)
This is awesome... but I have an extra challenge for you Matt... a while ago you assigned prime numbers to a number of your Patreons... get them to do the Collatz Conjucture with their number and see what happens. Hahaha
Matt, are there generalizations of the Collatz Conjecture? I suppose that you could define all possible similar algorithms, using different n, m, and p instead of 2, 3, and 1. For example: if x is disible by n, do it, else (x * m + p). I feel that mapping n, m and p and going to look how the series converge and after how much time they do it, would create some sort of very beautiful fractal, in the right hands 🙂
Yes! For some of them, it has iirc been shown that whether they always reach 1, is independent of (some axiom system, Idr which one(s)). Or possibly it is instead that for a certain family of such analogous versions, the task of deciding whether it always reaches 1 is undecidable? I don’t remember which one, but at least one of those.
@@luketurner314 if instead of generalizing to analogous rules one generalizes from integers to complex numbers, iirc there’s a way to get a fractal of some sort out of it. Iirc not one with much bulbousness to it though.
Does anyone know what the diagram @8:19 means? It looks like Zoe has given us a graph with unlabeled axes! For her introduction to the diagram, she says, "if I make the map that uses all of [the 1517 distinct numbers] once, what is it going to look like? So I got python to write me a little diagram; so I need to have some sense of where it was going to be very long, so that when I was making it I could make enough space for things." I don't understand how that diagram meets her need, or really what the "data" of the blue blobs are.
try polynomial f(x)=0 solving by consecutive equations, taking the feature of solutions f'(x)=0 giving the possible zero regions for newtons method, backtracking up to the 3+ degree equation, assuming you get the quadratic solution zeros to a 2nd degree polynomial derivative (insert the zeros the 3rd degree polynomial (either derivative or the original f(x)) then check if the points are +/- to have a zero between those derivative zero points
when I see "collatz" and "complete" in the same sentence I get a split second of shock
Me too
Me too! Would that be mathematical click bait? 😉
i was like "WAIT SOMEONE SOLVED IT???"
That wouldn't be a second channel thing. 😉
OMG SAME!
At 14:59, it shows 32 going to 8 when it should be 16, but don't worry everyone, it's fixed in the final poster.
Oh good. I was worried it'd ended up as a Parker poster.
and at 1:02, 50 is going to 151 instead of 25
1:13, Fantastic art but 50 is followed by 25, not 151. :-(
I didn't have the heart to spoil it for the kids, so am glad you did it :D
That initial python graph is actually quite pretty good design. Solid Album art.
4:58 hey, that's me! Thanks for putting my poster into the video
That binary one took a couple of goes - early version had a one bit error halfway through, so it got re-submitted!
I love how everyone who's looked into the Collatz conjecture will immediately recognize the number 9,232
True
What's special bout it?
@@Astromath It takes a long time to get to 1.
15:24/15:27 - suffice it to say this inspired me to have a fun little jaunt with some ruby code for generating a graphviz "dot" (or "twopi"; I played with both) file, and exploring what the directed graph could look like... with different colors based on size of number, even/odd status, and even for primes. Fun times! Thanks!
Fun to see a couple of contributions from my school pop up.
Very nice. I will be printing it out. I love that these kids have found such a great interest in math
What a great project to get school kids involved in math! (Or "maths" across the pond.) Thanks, Matt & Zoe! 👍
1:07 I like how they treated 50 as if it were odd
And it still reached 1
I can tell Zoe put a lot of effort into this
Did anyone else keep an eye on the clock on the wall behind them to look for time-jumps from the editing process?
Oh, a collabz.
Lovely work by all!
11:40 The IDs rounded to 1 decimal place had me confused for a while
They should have been declared as Int (or Integer, but starting at three digits, you don't get that big).
Damn I hadn't even heard when the conference was happening and where!
1:04 isn't it wrong from the step 50->151?
15:27 Is the offer to do every 3 digit number serious? I have time
Would be great to see!
1:10 50 -> 151 Hmm I guess 50 is odd now?
If I understand her @9:42 correctly, that is 2228 numbers for a super map with all 900 3-digit numbers. Would there be any 2- or 1- digit numbers missing from that super map? If "yes", which ones would be missing?
If "no", how many 3-digit numbers do you have to add to the super map (starting at 100 and going in numeric order) in order to have used all the numbers < 100?
I am not 100% sure if there is all 2 digit numbers in the map,
but I know that if you just multibly 2-digit numbers you will get every 2 digit number that way before 200, because biggest one is 99*2 =198 and second biggest are 98*2 or 49*2*2 = 196.
but is there way to get 99 before 198 if you start in order... No.
if you could, then you should be able to get it by from odd number that you would multible 3 times and add 1, but you can try that in reverse to 199
(199-1)/3 is not whole number, nor (199*2-1)/3, nor (199*2*2-1)/3 etc. there is always that 2/3 left over there.
so you need to go in order from 100 to 198, then you get every 2-digit number :)
(there is lot of useless numbers in between and I don't know what would be bethween [X-198] or shortest order around that 198 number, but probably lot shorter than 99 numbers)
The shadows cast by the down lights on the wall behind you make it look like you’re inside the mouth of a giant shark.
This is awesome... but I have an extra challenge for you Matt... a while ago you assigned prime numbers to a number of your Patreons... get them to do the Collatz Conjucture with their number and see what happens. Hahaha
Matt, are there generalizations of the Collatz Conjecture? I suppose that you could define all possible similar algorithms, using different n, m, and p instead of 2, 3, and 1.
For example: if x is disible by n, do it, else (x * m + p).
I feel that mapping n, m and p and going to look how the series converge and after how much time they do it, would create some sort of very beautiful fractal, in the right hands 🙂
That's a good idea. Sounds like great fun for the entire afternoon, too!
Google fractran
Yes! For some of them, it has iirc been shown that whether they always reach 1, is independent of (some axiom system, Idr which one(s)). Or possibly it is instead that for a certain family of such analogous versions, the task of deciding whether it always reaches 1 is undecidable? I don’t remember which one, but at least one of those.
Why do I get the feeling that if that were graphed it would look similar to the Mandelbrot Set?
@@luketurner314 if instead of generalizing to analogous rules one generalizes from integers to complex numbers, iirc there’s a way to get a fractal of some sort out of it. Iirc not one with much bulbousness to it though.
god damnit the title had me fooled lmao
See Matt's eyes light up when tables are involved.
Brilliant!
Does anyone know what the diagram @8:19 means? It looks like Zoe has given us a graph with unlabeled axes! For her introduction to the diagram, she says, "if I make the map that uses all of [the 1517 distinct numbers] once, what is it going to look like? So I got python to write me a little diagram; so I need to have some sense of where it was going to be very long, so that when I was making it I could make enough space for things."
I don't understand how that diagram meets her need, or really what the "data" of the blue blobs are.
I believe it's a graph in the nodes-and-edges sense, not in the x-and-y axes sense. It shows the shape of the total supermap.
It's a map, it's all the numbers connected. Like the final poster, but obviously not as artistically made.
You should do another Christmas tree light video
Hi Matt, could you share the Python code used to create the graphs? Thank you
The code is linked to in the video description/notes.,
@@zoegriffiths1308 Thank you
Looks great
Been working on it for months... I almost got a heart attack. But loved this nonetheless
I was going to send one in, but I picked a number that didn't go to 1. Sorry.
1:06 50 going to 151? :P
pretty cool!
Hey Matt, I wish you had more properly introduced your colleague, Zoe Griffiths, at the start of this video.
try polynomial f(x)=0 solving by consecutive equations, taking the feature of solutions f'(x)=0 giving the possible zero regions for newtons method, backtracking up to the 3+ degree equation, assuming you get the quadratic solution zeros to a 2nd degree polynomial derivative (insert the zeros the 3rd degree polynomial (either derivative or the original f(x)) then check if the points are +/- to have a zero between those derivative zero points
Collatzb
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