This is actually an example of hyperbolic growth, where it reaches infinity in a finite time. In this simulation, each doubling takes roughly half the time than the previous one, which sums up to a finite time.
And yet it will still never reach infinity. Even if the simulation runs until the last black hole evaporates into radiation, even if it runs for one trillion to the trillionth power of years, it will still not be infinite. Infinity is, by nature, not ever achievable or reachable
That's not exponential growth in time though. If the time between corner bounces is inversely proportional to the number of squares, it's gonna take half as much time on average as it previously did. So it'll grow exponentially at an exponentially faster rate. If we call f(t) the function that gives the number of cubes at time t, we know that f(1+1/2+1/4...+1/(2^n)) = 2^n, with n being the number of bounces. So f(2-(1/2)^n)= 2^n. Changing the variable just to make it nicer, f(2-(1/2)^n)=2^n f(2-1/(2^n))=2^n f(2-1/x)=x f(2-x)=1/x f(2-(2-x))=1/(2-x) f(x)=1/(2-x) Adding a factor of 2 to account for the fact that we start with one square, we get f(t)=2/(2-t) on average. It means that the number of balls does *not* grow exponentially with time, but actually hyperbolically !
The number of squares at the end is equivalent to 2^x since x=14 then it become 2^14 and 2^14 is equal to 16 384👍 Btw x is the number of time a square hit a corner you can see it at the bottom referencing to the line "corner hit: x"
Okay, so the formula for the chance of corner bounces here is (n/s)/4 where n is the amount of cubes and s is the seconds of the short, which is 60. So according to the end, having 16,384 squares, the chance of a square hitting the corner is ~63.8% for each square. I just started simple algebra, by the way.
A few balls, triangles, and squares bouncing off a ring, if lets say, a ball touches a square, theres a 50% chance one turns into the other, making either 2 squares or 2 balls, and this happens until theres only triangles, squares, or balls left.
With y being the amount of squares at the end and x being the amount of corners hit, we can use a simple formula to calculate the amount of squares with each corner hit The formula being Y = 2^x So at the end, the amount of squares before it crashed would be Y = 2^14 2^10 = 1024 2^11 = 2048 2^12 = 4096 2^14 = 16384 So at the end there’s a total of 16384 squares on the screen before it crashed
Think about it. The first 10 seconds we got like 3-4 hits. But when there’s like 200 of them, it takes like 1000 bounces before we got another. That’s some insane luck we had
Technically since that is a square area in which the smaller squares bounce around in, hitting the corner would mean you hit the opposite corner after every collision, so the corner was never truly hit in this case, therefore it would remain one square bouncing around aimlessly forever
@@Gokuirby No, it wouldn't. Come on, can't you imagine a little square getting a perfect hit at the corner while sliding at 30 degrees? Surely you can imagine a tiny square starting exactly at the corner and leaving it at 30 degrees. Now just let it go backwards... ;P
As someone who isn't a nerd, ill try to say it the best i can. So each time you x2 and that happened 16 times. So not 1x16 but 1x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2. But i don't feel like doing the math though. Hope that helps someone.
I've seen a lot of circles where the bottom makes it shrink but the top makes it grow. What about the top makes it shrink while the bottom makes it grow?
It would get so big that the ball wouldn’t be able to hit the top, making it just grow more. You’d need another factor like speed increasing at a faster rate per bounce to solve that issue.
If i counted right it doubled 12 times wich means theres 4,096 squares on the screen this is found by the equation 1×2^12. Explination↓ The basic equation for exponential growth is a×b^c; a is the amount started with or base amount, b is how much bigger it gets every time (2 for doubled, 3 for tripled, 4 for quadrupled, ect.), c is how many times it gets bigger. (a, b, and c are just place holders since i don't know the correct variables)
At the end there was 2^15 or 32k squares (because of the last bounce), because of the small fps it would take a lot of time to add 1 to the corner hits, but the sound was there so its 2^15 Edit:there was probably more than 2^14 or 2^15 because the chance of each square hitting the corner is around 60%, so its probably like 2^(16000) at the end, or 2^31,or 2^63,or 2^1024
What are the bounce physics? As a perfect square will result in the object filling the same unchanging pattern so unless they start in the corner they will never hit the corner
![Lp. Сердце Вселенной #60 РОЖДЕНИЕ ЛОЛОЛОШКИ [Финал] • Майнкрафт](http://i.ytimg.com/vi/YoR0pAV9FVQ/mqdefault.jpg)
How many squares are there at the end? 🤔
At least 8
Now get a better computer and see how many squares we can get then
Infinite, but you can't see them
8192?
32,768, to be exact?
Hello don’t ignore this comment!
Now add collision 😈
"Now make it angrier"
@@ShinyDitto hahahaha that's a good reference
I thought there was collision when the first two went through each other
@@ShinyDittoLOL
@@Capital_3I don't mean to be ride, but you know collision means touch right? I don't understand what you're saying.
I’m not no expert, but i reckon there’s at least 10 squares there
"How mattresses do you think there are Patrick?"
"...10"
@@Anothertickinthewall i loved that scene
Damn, that’s got to be more than four.
@@bazookablastoff6447That's AT LEAST 1
r/technicallythetruth
Roses are red
Cacti are prickly
Holy shit that escalated quickly
Man, I was gonna use that
Im adding that to my list of weird phrases
@@Joe_PottsSame
Roses are red cacti are prickly holy s*** that escalated quickly
@@kimberlypierson5760 why do you censor it?
This is actually an example of hyperbolic growth, where it reaches infinity in a finite time. In this simulation, each doubling takes roughly half the time than the previous one, which sums up to a finite time.
The Supertask.
And yet it will still never reach infinity. Even if the simulation runs until the last black hole evaporates into radiation, even if it runs for one trillion to the trillionth power of years, it will still not be infinite. Infinity is, by nature, not ever achievable or reachable
Asymptotic?
no it, approaches 1. use infinite geometric sequence formula
@@mr.nose_hairyt7937 whatever the unit is, it results in a finite time.
A square bounces faster and every hit the border shrinks faster
The first square hits a corner in seconds but the DVD screen saver doesn’t for literal hours.
dvd found an enemy ☠️
UNDERRATED comment ☠️
👍@@BPR_Blurry5639
I'm scared
That's not exponential growth in time though. If the time between corner bounces is inversely proportional to the number of squares, it's gonna take half as much time on average as it previously did. So it'll grow exponentially at an exponentially faster rate.
If we call f(t) the function that gives the number of cubes at time t, we know that f(1+1/2+1/4...+1/(2^n)) = 2^n, with n being the number of bounces.
So f(2-(1/2)^n)= 2^n. Changing the variable just to make it nicer, f(2-(1/2)^n)=2^n
f(2-1/(2^n))=2^n
f(2-1/x)=x
f(2-x)=1/x
f(2-(2-x))=1/(2-x)
f(x)=1/(2-x)
Adding a factor of 2 to account for the fact that we start with one square, we get f(t)=2/(2-t) on average. It means that the number of balls does *not* grow exponentially with time, but actually hyperbolically !
Yeah someone else have already said that this was "an example of hyperbolic growth"
You just figured out the formula, nice job!
👏
@@nopinias69 I don't claim to be the first one, though, with hundreds of comments there's bound to be at least one who got it before me.
@@givrally I know, I just wanted to say "good job" for having supported conclusion with a formula that demonstrates this results
🤓
@@coltoncheong273someone get the trash disposal we have a broken record
SQ = square
The collisions (corner hits)
There are 16.38 SR in total
The fact that the 64 lasted so long is crazy
theres not enough people talkimg about how amazing the sound on these videos is
I was ready for it to take literally forever before it hit a corner.
There were 14 corner hits and thus 14 duplications until crashing, which means it is 2^14 which is equal to 16384.
The corner collision sound…😩🎶💯
The number of squares at the end is equivalent to 2^x since x=14 then it become 2^14 and 2^14 is equal to 16 384👍
Btw x is the number of time a square hit a corner you can see it at the bottom referencing to the line "corner hit: x"
Okay, so the formula for the chance of corner bounces here is (n/s)/4 where n is the amount of cubes and s is the seconds of the short, which is 60. So according to the end, having 16,384 squares, the chance of a square hitting the corner is ~63.8% for each square.
I just started simple algebra, by the way.
You are not mathematically inclined are you
Man this is the Anti-🤓
2^(n-1), so 8,192 at the end
@@TheMagicat It's still 2^n because assuming n is the amount of corner hits it starts at 0, 2^0 = 1
So it's 2^14 = 16384
This started as a slowed down version of we're number 1 then turned into chaos
A few balls, triangles, and squares bouncing off a ring, if lets say, a ball touches a square, theres a 50% chance one turns into the other, making either 2 squares or 2 balls, and this happens until theres only triangles, squares, or balls left.
I love the sound made when a cube hits the corner
Not only does the amount of squares double, but the likelihood of a corner being hit increases as well.
Do one where a cube in a square, if the cube bounces another cube is added, if a cube hits the corner a random cube is removed
If this was a screen saver it would have been one square for the whole minute.
the sound when a square hits a corner has immense comedic property. the reverb is cracking me up.
That escalated faster than twitter
did anybody else just try to track the first square only to see it did nothing past the first corner bounce
That green yellow and red caught me off guard, they all were going together like traffic lights.
If this was the dvd screen saver there would still only be one cube 😂
Nah the sound when it hits the corner sounds like the pacer test
With y being the amount of squares at the end and x being the amount of corners hit, we can use a simple formula to calculate the amount of squares with each corner hit
The formula being Y = 2^x
So at the end, the amount of squares before it crashed would be Y = 2^14
2^10 = 1024
2^11 = 2048
2^12 = 4096
2^14 = 16384
So at the end there’s a total of 16384 squares on the screen before it crashed
that should be 2^13 which is ~8,200 squares… That shouldn’t be too difficult to compute for most computers-
The fact that the oragne and blue blocks stayed together the whole time is crazy. They get together at the fourth hot
The sound of the corner is straight up from garten of banban
We went through this before with the balls. Now history shall repeat with you adding collision.
I followed the first one for as long as I could
I thought this was going to be like the old DVD player meme where it never hit the corner
You should make the squares collide next time
Can i just say the sohnd deisgn is killer here. The corner hit sound is what a corner hit feels like whenever you see one
exponential growth : let's say that x(1) is equal to 2 now 2^x = x it's a recursive equation so it explodes to infinity.
Weirdly chaotic and calming at the same time
Start: First time using note blocks
Middle: Minecraft music
End: Game crashed
Think about it. The first 10 seconds we got like 3-4 hits. But when there’s like 200 of them, it takes like 1000 bounces before we got another. That’s some insane luck we had
This should be a screen saver. Instead of crashing, maybe do a restart function when some number is calculated as error? Maybe it could work.
do you want a cpu benchmark as a screen saver
Do it a gain but with collision
The pattern makes me feel like I'm playing the mario 64 ds wanted minigame
This would be way more impressive if there was particle-particle collision.
Technically since that is a square area in which the smaller squares bounce around in, hitting the corner would mean you hit the opposite corner after every collision, so the corner was never truly hit in this case, therefore it would remain one square bouncing around aimlessly forever
Why would hitting the corner mean you hit the opposite corner after every collision? The trajectories are not at 45 degrees to the sides.
@@adayah2933 because it's a square area, and the object is also square, so hitting the corner means angle at which it goes back would be 45 degrees
@@Gokuirby It will go back at the same angle that it came at, not 45 degrees.
@@adayah2933 it would have to be 45 degrees to hit the corner tho in a square box 😭
@@Gokuirby No, it wouldn't. Come on, can't you imagine a little square getting a perfect hit at the corner while sliding at 30 degrees?
Surely you can imagine a tiny square starting exactly at the corner and leaving it at 30 degrees. Now just let it go backwards... ;P
Pacer test flashbacks
When there was 4 corner hits, the song was sooo relaxing
the blue and orange square staying together lol
As someone who isn't a nerd, ill try to say it the best i can. So each time you x2 and that happened 16 times. So not 1x16 but 1x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2. But i don't feel like doing the math though. Hope that helps someone.
This should be a screen saver
actually, this is “not exponential” growth as the time between doubling decreases and some balls hitting the corners did not double.
I was able to follow the original one
S = The number of squares in the simulation
C = The number of times the squares hit the corner
S = 2^C
Used to wait minutes for the screensaver to hit the corner. Now its instant
The key to keeping up is not to keep track of the squares but the counors
The start of this video is how my brain works and when the block hits the corner I experience a thought
I honestly dare you to do this but the squares can collide with each other
finally, this type of video but it ACTUALLY crashes
since we see 14 corner hits and 3 at the end that we cant see then this means that the amount of squares would be 131,072
finally get to see some corner hits 😮
Try keeping your eye the first one that appeared on the screen
I've seen a lot of circles where the bottom makes it shrink but the top makes it grow. What about the top makes it shrink while the bottom makes it grow?
It would get so big that the ball wouldn’t be able to hit the top, making it just grow more. You’d need another factor like speed increasing at a faster rate per bounce to solve that issue.
Idk why but when the cubes passed through each other i felt like i had a system reset like my brain couldn't handle it 💀💀
Please I really want to know how you create these they look so damn cool and so satisfying just give us a tutorial video!!!
At one point, it started to sound like the little music you hear when you get the hammer in Donkey Kong arcade🤣
I was waiting for an explosion, but luckily, there was no jumpscare this time. 😅
Turns out the most fun we get from computers is seeinf them fail
i used to watch the DVD thing bounce for 10 minutes and this square does it right away
Finally there’s one of these that hit the corner
This tickles my brain the right way
My mum said, 'Jesus Christ is that Picasso?'
I'm crying right now 🤣💀🤣
Video idea: whenever a ball collides another one spawns, but if it touches the top one of the balls disappear
ya always let it crash, its more fun when there is so many, it slows down and goes silent due to freezing
If i counted right it doubled 12 times wich means theres 4,096 squares on the screen this is found by the equation 1×2^12.
Explination↓
The basic equation for exponential growth is a×b^c; a is the amount started with or base amount, b is how much bigger it gets every time (2 for doubled, 3 for tripled, 4 for quadrupled, ect.), c is how many times it gets bigger.
(a, b, and c are just place holders since i don't know the correct variables)
At the end there was 2^15 or 32k squares (because of the last bounce), because of the small fps it would take a lot of time to add 1 to the corner hits, but the sound was there so its 2^15
Edit:there was probably more than 2^14 or 2^15 because the chance of each square hitting the corner is around 60%, so its probably like 2^(16000) at the end, or 2^31,or 2^63,or 2^1024
2^(n-1), so 8,192 right before the end of the
WINDOWS.EXE has crashed
At least 16,384. Because the corner counter at the bottom says 14, so you do 1 X 2 then, answer X 2 for a total of 14 times
Yes, in other words, 2^14
"the number of squares doubles with every corner hit."
*Never hits a corner*
if you consider 14 to be then end then 16384 is the answer
the formula would be f(x) =1(1+1)^{14}
MFGDHHH THE SOUND IT MAKES WHEN IT HITS A CORNER
THE NOISE WHEN IT HITS THE CORNER
It's fake, we all know it never truly hits the corner
Theres way more corner hits than i expected early on
You know we all were trying to find the square that caused it on that third one and we still missed!
It actually becomes 2^29482850259283813, it just cant double that much in an amount of time like the end of the video.
So that's why the DVD logo never touches the corner
This guy is relaxing than SATISFYNG balls that just plays that goddamn kerosene song and every video is kerosene
I was expecting it to take way longer than it actually did
I wish the DVD icon did that all the time it would be so satusfying
Win7 crashed after million squares
What are the bounce physics? As a perfect square will result in the object filling the same unchanging pattern so unless they start in the corner they will never hit the corner
Some corner hits were iffy though
Fitness gram passer test PTSD when it hit the corner
Pov:When the DVD logo hits the corner OH MY GOD!!
The end is literally 1000+ errors appearing in your computer 💀
idea: it will be 6 balls bouncing but every bounce gets faster
Dunder Mifflin employees absolutely losing it right now
This is actually frustrating to watch at the start and still is because of lag.