Tibees has a level of talent and intelligence that I wish Tailor Swift would emulate. Because Tibees contributes to Humanity, whereas Tailor Swift does not, I think Tibees should be the more popular star!
What's funny about that? The name has nothing to do with almond bread, but everything to do the name of the mathematician who invested so much time on the phenomenon, he ended up branding his name on it?
@@lewis7515yes, but what they’re saying is his surname translates in German to almond bread. Which might say something amusing about the profession of his familial ancestors.
@@Tasorius the agents of the 4th Dimension speak in gentle, unassuming voices so that you do not remember the scientific content and revolutionary knowledge unless your brain is inclined to it /j
Another thing to look at is the relationship between the Mandelbrot set and the family of quadratic Julia sets. The Mandelbrot Set can be seen as a "map" of these Julia sets. They share the same formula (z=z² + c), but while c in the Mandelbrot set is the starting point, in the Julia sets, the initial value for z is the starting point, and C is a constant for the entire image. Thus, each point C in the Mandelbrot maps to an entire image in the Julia. A point inside the Mandelbrot will generate a fully-connected Julia. A point outside the Mandelbrot will generate a disconnected Julia. The closer a point is to the border of the Mandelbrot, the more intricate the corresponding Julia will be. 2 special cases where the Julia set is not a fractal are: c=0, and c=-2. It's not known if there are other non-fractals.
The song always helped me: 🎶 Just take a point called Z in the complex plane 🎵 Let Z1 be Z squared plus c, 🎶 Let Z2 be Z1 squared plus c, 🎶 Let Z3 be Z2 squared plus c, 🎶 🎵 and so on If the series of Zs should always stay Close to c and never trend away.. That point is in the Mandlebrot set🎵🎶🎵
@@EllipticGeometryNew new kindergarten covers quantum physics, general relativity, bayesian statistics, and chaotic systems. The graduation project is developing cure for cancer.
Try watching a Mandelbrot zoom on TH-cam for 5 minutes straight. I can't guarantee that you will survive, or that your vision won't be permanently weird... The faster it goes, the more dangerous it is. I got away with just a phobia of Mandelbrots, and I was one of the lucky ones...
The Secret Life of Chaos was my first intro to fractals beyond common parlance. Was very cool to see the backstory of Mandelbrot, and how he was the first to use computers to create fractal images. Highly recommend that documentary!
I've loved the Mandlebrot ever since learning about it in high school. Even made a calculator app to generate it. One thing for anyone wondering, to figure out if a point goes towards infinity (bails out) or not, you take the 2 numbers and get the square root of them squared and added together. 2+3i becomes sqrt(4+9). And a bail out value is determined, For the. Mandlebrot, that's usually 4. If it bails out, it's not part of the Dark Inner region
It's my worst nightmare. I once looked at it zoom in like that for 5 minutes, and my vision was weird for about an hour, with everything appearing to become bigger and smaller. So it scares me now...
@@stapler942I didn't say that real numbers are not natural, what I meant to say is that real numbers seem like a simplification of the perception of reality and complex numbers seem to show reality in more profound ways. For example, complex numbers have the idea of "rotation" as part of its structure and this makes them indispensable for a complete description of Nature in a 3D + time universe. I believe that is possible to divide mathematics into natural and non-natural parts, in the sense of being connected to Nature or being a purely mental game not necessarily related to anything. I believe the idea of fractals is still incomplete.
Did you know? The Mandelbrot set is a 2D cross-section of a 3D graph, with the Bifurcation graph representing another 2D cross-section. Veritasium did a video on it.
Want to begin with designing a calculator with only your grammar school education? Use 3 counters 2 of which only count down ( counters 2 & 3). Counter 1 counts up and down. Positively and negatively. For addition counter 1 counts up and counter 2 counts down at the same time . When counter 2 equals zero the sum is the contents of counter 1. For subtraction the same except both counters count down. For multiplication counter 1 is transferred to counter 3 then cleared to zero. Next each time counter 1 is added to counter 2 counter 3 is decreased by 1 until counter 3 equals zero. For division counter 1 is used to count the number of times counter 2 can be subtracted from counter 3. The answer is always in counter 1 and counter 2 is reloaded as needed.
Also, in many representations of the set, the other colors indicate how quickly a number grows, so for instance the lighter a shade, the faster the number approaches infinity.
I like how she talks about math I don't understand in any way, like my mom used to read fairy tales to me when I was a kid. Sort of like she is reading the Blue Fairy Book, but written by George Polya.
Mandelbrot was an inexhaustible self-promoter who could snow/bamboozle the liberal arts majors running IBM, which provided a perch for him to shout his own praises. He was given time in serious circles due to the possibility of corporate largess being given to legitimate researchers. It was also the time in the early 80s, when computer graphics first came to the fore, that flashy pictures could be made and create a sense of awe around his work. All the original work was done in the late 19th and early 20th centuries when real analysis was making strides in measure and particularly covering theorems. Look up Hausdorff measure for the real work.
So you mean to say, pick a point called c in the complex plane, z₁ is c²+c, z₂ is z₁²+c, z₃ is z₂²+c and so on. If the series of z's never tends away, that point is in the mandelbrot set. (This is a song)
Perhaps i misunderstood, but squaring a number, adding it to itself and repeat that with the result, by definition gives you an infinite amount of numbers
Potential video idea: what would a human look like to a 4th or 5th dimensional being? Don't we also exist in the 4th/etc dimensions, even if we can't perceive it? Based on your videos across the years, my guess is: yes we do, and you'd probably look infinitely pretty 🌌
Wonder why no one visualizes the dark outside of the Mandelbrot, that is visualizing the real & imaginary parts as colors like normalized blue & green as they explode to infinity, its actually more interesting
Did you know: the B in Benoit B Mandelbrot stands for Benoit B Mandelbrot.
It's painful.
But what does the B in Benoit B Mandelbrot stand for?
@@robocomboBenoit B Mandelbrot
So this is what a Mandelbrot set actually is
@@thecringequeen31 then what does the B stand for in Benoit B Mandelbrot?
Thank you for the explaination, i always wondered how Mandelbrot worked (funny enough, the name means "almond bread" in german)
Tibees has a level of talent and intelligence that I wish Tailor Swift would emulate. Because Tibees contributes to Humanity, whereas Tailor Swift does not, I think Tibees should be the more popular star!
What's funny about that? The name has nothing to do with almond bread, but everything to do the name of the mathematician who invested so much time on the phenomenon, he ended up branding his name on it?
@@lewis7515yes, but what they’re saying is his surname translates in German to almond bread. Which might say something amusing about the profession of his familial ancestors.
@@ricardolobos673
You’re complaining about Taylor? What about Miley Cyrus, Niki Minaj and other bad apples that are FAR worse for society!
@@BassotronicsLearn tolerance, you'll become a worthwhile being.
Zoom animations for the Mandlebrot set are fun. Infinite detail with repeating patterns; almost like a cosmic secret is being revealed.
🦠
Math is the language of the universe 😊
🧑🏾🚀.
3seconds and her voice puts me to sleep or hypnotizes me
My mind turns it off so that I don’t hear her.
@@KJKP A very old defence mechanism that protects you from eldritch horrors, to a certain point... Don't trust it too much...
Many have fallen into the fourth dimension when being hypnotized like that...
Thought I was alone
@@Tasorius the agents of the 4th Dimension speak in gentle, unassuming voices so that you do not remember the scientific content and revolutionary knowledge unless your brain is inclined to it /j
Said in such a soothing way. I wish you had been my math teacher 👩🏫💖
Another thing to look at is the relationship between the Mandelbrot set and the family of quadratic Julia sets. The Mandelbrot Set can be seen as a "map" of these Julia sets.
They share the same formula (z=z² + c), but while c in the Mandelbrot set is the starting point, in the Julia sets, the initial value for z is the starting point, and C is a constant for the entire image. Thus, each point C in the Mandelbrot maps to an entire image in the Julia. A point inside the Mandelbrot will generate a fully-connected Julia. A point outside the Mandelbrot will generate a disconnected Julia. The closer a point is to the border of the Mandelbrot, the more intricate the corresponding Julia will be.
2 special cases where the Julia set is not a fractal are: c=0, and c=-2. It's not known if there are other non-fractals.
Thank You for the explanation!
Very nice! Thank you!
Thanks. I got a C in that class last year. I remember this. Sad memories. Lol
I never knew that this mandelbrot pattern had to do with numbers. Thanks for teaching me I appreciate it.
All patterns have to do with numbers 😀
The song always helped me:
🎶 Just take a point called Z in the complex plane 🎵
Let Z1 be Z squared plus c, 🎶
Let Z2 be Z1 squared plus c, 🎶
Let Z3 be Z2 squared plus c, 🎶
🎵 and so on
If the series of Zs should always stay
Close to c and never trend away..
That point is in the Mandlebrot set🎵🎶🎵
Tibees + 3blue1brown collab when?
I'd like to see a collab between Tibees and Domotro from Combo Class. I think the mixture of calm and chaos would be interesting...
One of the most straightforward explanations of the Mandelbrot set I’ve ever heard. Thanks!
Super pertinent for most people. Thank you. Explained so well.
This is so helpful and interesting. Too much that I shared it with aeronautical engineering colleagues group chat. Virtual hugz from Mexico 🇲🇽
You have the energy of an happy talking about the mysterious of the universe, but because you talk about the actual math involved, that’s pretty cool
I just like how it means almond bread
I didn't understand a word of that, but I feel so calm and relaxed now!
You are my favorite kindergarten teacher. ❤
bro my mind would melt if she was my kindergarten teacher.
Kindergarten? I don’t think they covered fractals there, even superficially. But with the new new math, who knows.
@@strawberrygoldie329 a while ago someone said her videos feels like the first day in a 4th dimension kindergarten.
@@EllipticGeometryNew new kindergarten covers quantum physics, general relativity, bayesian statistics, and chaotic systems. The graduation project is developing cure for cancer.
Tibees is the type of person to give us weekly math facts and still can make them entertaining😄
The 'beetle' has always reminded me of some Crop Circles
Cheers. I still haven’t got a clue. But I’m all for it. What time does it start?
I think it's at 5pm today
Been here for years, haven't learned any actual science but it is relaxing.
Try watching a Mandelbrot zoom on TH-cam for 5 minutes straight. I can't guarantee that you will survive, or that your vision won't be permanently weird... The faster it goes, the more dangerous it is. I got away with just a phobia of Mandelbrots, and I was one of the lucky ones...
@@Trevil666 Looks like you are either ready to fall into the 4th dimension, or you are immune...
Thanks for the summary, it is nicely organized. ✨✨
I could listen to her voice for hours...
I feel like this represents the shape of the universe
She's such a smart cookie! 👏 ❤
I really enjoyed your guest season on Jet Lag! You were brilliant!
I finally get it! Thank you for a very clear and succint explanation.
Neat and elegant! Thanks Tibee!
This is my favourite ASMR channel.
Nothing frames a pretty picture, and the ability for us to stand apart and watch together in the 4th Dimension.
Thank you for introducing me to this topic
I find that understanding the Mandelbrot set starts with understanding the Mandelbrot set.
To understand recursion you need to understand recursion 🤣🤣🤣
Thanks for that important detail. I never realised this.
Oh its the nice math lady that does shorts that send me sprialing into existential terror
The Secret Life of Chaos was my first intro to fractals beyond common parlance. Was very cool to see the backstory of Mandelbrot, and how he was the first to use computers to create fractal images. Highly recommend that documentary!
Excellent work, thanks
If you struggled with this, there's a song about this as well by Jonathan Coulton which may help.
I've loved the Mandlebrot ever since learning about it in high school. Even made a calculator app to generate it. One thing for anyone wondering, to figure out if a point goes towards infinity (bails out) or not, you take the 2 numbers and get the square root of them squared and added together.
2+3i becomes sqrt(4+9). And a bail out value is determined, For the. Mandlebrot, that's usually 4. If it bails out, it's not part of the Dark Inner region
I never thought about this. Now that you mention it, it's cool
Your voice is amazing!
I only ever see these when I'm high and you just keep blowing my goddamn mind. If you're a Four Dimensional being, you can say so 😂
It's my worst nightmare. I once looked at it zoom in like that for 5 minutes, and my vision was weird for about an hour, with everything appearing to become bigger and smaller. So it scares me now...
One guy says it's proof that God exists.
Complex numbers are fascinating, they seem more "real" (more natural) than "real" numbers
Would you say then that rational numbers are more "natural" (integral) than natural numbers? 😉
@@stapler942I didn't say that real numbers are not natural, what I meant to say is that real numbers seem like a simplification of the perception of reality and complex numbers seem to show reality in more profound ways. For example, complex numbers have the idea of "rotation" as part of its structure and this makes them indispensable for a complete description of Nature in a 3D + time universe. I believe that is possible to divide mathematics into natural and non-natural parts, in the sense of being connected to Nature or being a purely mental game not necessarily related to anything. I believe the idea of fractals is still incomplete.
@@frangershwing I'm being facetious by extending the pun space, don't mind me.
Thank you Toby!
Did you know? The Mandelbrot set is a 2D cross-section of a 3D graph, with the Bifurcation graph representing another 2D cross-section. Veritasium did a video on it.
Your explanation ❤
How amazing!!!
Staring into the infinity of your eyes... oh, the Mandelbrot set is nice too...
Want to begin with designing a calculator with only your grammar school education? Use 3 counters 2 of which only count down ( counters 2 & 3). Counter 1 counts up and down. Positively and negatively. For addition counter 1 counts up and counter 2 counts down at the same time . When counter 2 equals zero the sum is the contents of counter 1. For subtraction the same except both counters count down. For multiplication counter 1 is transferred to counter 3 then cleared to zero. Next each time counter 1 is added to counter 2 counter 3 is decreased by 1 until counter 3 equals zero. For division counter 1 is used to count the number of times counter 2 can be subtracted from counter 3. The answer is always in counter 1 and counter 2 is reloaded as needed.
I could listen to you infinitely
By the way,
How can you keep a smile on your face forever?
Your smile is cutest one 😊
Maths ASMR ❤ her voice is just 🙌
The Mandelbrot set was actually what piqued my interest in mathematics. I studied extensively, and wrote several software to plot it.
This causes me such joy
ASMR Science. Thank you.
My favorite part of looking at the boundary is that it's the closest we'll get to glimpsing the infinitesimal 😗👌
My mind went to nyquist plots that I had studied in my past😊😊😊😊
As a kid of 13 i used my simple calculator to calculate the numbers of a Mandelbrot-Männchen and draw it on a paper.
The Mandelbrot Set is caked up
Amazing explaining
Also, in many representations of the set, the other colors indicate how quickly a number grows, so for instance the lighter a shade, the faster the number approaches infinity.
But u r adding it to 1 in the video..
This is my favorite thing.
Important note here though: it's not that numbers less than 1 always get smaller because 0 would stay the same and negative numbers would get bigger
Science aside, that voice is actually soothing
her: "so about the mandelbrot set"
me: *asmr induced coma*
I like how she talks about math I don't understand in any way, like my mom used to read fairy tales to me when I was a kid. Sort of like she is reading the Blue Fairy Book, but written by George Polya.
Mandelbrot was an inexhaustible self-promoter who could snow/bamboozle the liberal arts majors running IBM, which provided a perch for him to shout his own praises. He was given time in serious circles due to the possibility of corporate largess being given to legitimate researchers. It was also the time in the early 80s, when computer graphics first came to the fore, that flashy pictures could be made and create a sense of awe around his work. All the original work was done in the late 19th and early 20th centuries when real analysis was making strides in measure and particularly covering theorems. Look up Hausdorff measure for the real work.
That's interesting.
I have watched those Mandelbrot zoom videos so many times, but never understood how it works😅
If I wanted to listen to an ASMR voice, I probably would have googled that.
I never thought I'd be happy to see some numbers being abducted to the Mandlebrot set but here we are... 😂
Where were you,when I was learning math?❤
The only rule for existing is don't be the set that destroys it's relevance
Proper analysis
Because all is one
It’s crazy to think that every time you zoom in on any type of fractal, it gets more and more detailed. This explaining the Theomertmalagos😅
Her voice sounds like soft wind chimes.
So you mean to say, pick a point called c in the complex plane, z₁ is c²+c, z₂ is z₁²+c, z₃ is z₂²+c and so on. If the series of z's never tends away, that point is in the mandelbrot set.
(This is a song)
I wonder if the Mandelbrot set could have some form of application in the real world.
Its every where. Mandelbrot set is fractal math
Yes! It does!! In so many things! Look at the replicating pattern in a pine cone, it is all throughout the world in many different things.
Perhaps i misunderstood, but squaring a number, adding it to itself and repeat that with the result, by definition gives you an infinite amount of numbers
I like understanding you.
Thank you
Amazing content. Happy to subscribe for more 😊
Mandelbrot! Mandelbrot! Mandelbrot!
Almond bread xd or is it a bakery item idk
@bleanG I guess there aren't many Seinfeld fans here. 🤣 🤣 🤣
@@iheardthat1b4 yeah lol
The German word Mandelbrot translates to almond bread
The thing that shows the set best is rotating the plot in 3d to show that's it's just a contour plot
Interesting!
I wish my battery life was longer so I cold listen for hours
When are you gonna be a guest on Countdown? 😍😍😍😍😍
"Pathological monsters!"
Arthur C Clarke made an excellent documentary on this called The Colors of Infinity with Mandelbrot himself
Hey Tibees,
Just Wanted You To Know
"If Beauty Was A Function,
You'd Be An (e^x)ponential One..."
2 words. SO COOL. 😁👍
Potential video idea: what would a human look like to a 4th or 5th dimensional being? Don't we also exist in the 4th/etc dimensions, even if we can't perceive it?
Based on your videos across the years, my guess is: yes we do, and you'd probably look infinitely pretty 🌌
Wonder why no one visualizes the dark outside of the Mandelbrot, that is visualizing the real & imaginary parts as colors like normalized blue & green as they explode to infinity, its actually more interesting
Numbers less than one BUT GREATER THAN -1 get smaller when you square them
Do you have an audio book because I can listen to this voice forever.
-2 is smaller than 1 and gets larger, not smaller, when you square it.
By the way Benoit autobiography is great... Is an amazing story of survival and unconformity... The Fractalist
I can see that. Thanks.
It’s known as the finger print of god. It’s found everywhere in nature.
She makes me think 🤔....🖤🌑🕶️🔥