So what is the Mandelbrot set anyway?

[@Andrews__YT]

Did you know: the B in Benoit B Mandelbrot stands for Benoit B Mandelbrot.

[@lewis7515]

It's painful.

[@robocombo]

But what does the B in Benoit B Mandelbrot stand for?

[@thecringequeen31]

@@robocomboBenoit B Mandelbrot

[@FirstSynapse]

So this is what a Mandelbrot set actually is

[@moodonut]

@@thecringequeen31 then what does the B stand for in Benoit B Mandelbrot?

[@Keradurakh]

Thank you for the explaination, i always wondered how Mandelbrot worked (funny enough, the name means "almond bread" in german)

[@ricardolobos673]

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!

[@lewis7515]

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?

[@nickcara97]

@@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.

[@Bassotronics]

@@ricardolobos673 You’re complaining about Taylor? What about Miley Cyrus, Niki Minaj and other bad apples that are FAR worse for society!

[@andhewonders]

​@@BassotronicsLearn tolerance, you'll become a worthwhile being.

[@bryangreen6231]

3seconds and her voice puts me to sleep or hypnotizes me

[@KJKP]

My mind turns it off so that I don’t hear her.

[@Tasorius]

@@KJKP A very old defence mechanism that protects you from eldritch horrors, to a certain point... Don't trust it too much...

[@Tasorius]

Many have fallen into the fourth dimension when being hypnotized like that...

[@dubistverrueckt]

Said in such a soothing way. I wish you had been my math teacher 👩‍🏫💖

[@BleuSquid]

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.

[@sheep1ewe]

Thank You for the explanation!

[@thecrowsnest6963]

Very nice! Thank you!

[@johnlime1469]

Thanks. I got a C in that class last year. I remember this. Sad memories. Lol

[@zeruzio1345]

Tibees + 3blue1brown collab when?

[@murphybed7919]

I never knew that this mandelbrot pattern had to do with numbers. Thanks for teaching me I appreciate it.

[@polycrystallinecandy]

All patterns have to do with numbers 😀

[@niravelniflheim1858]

Zoom animations for the Mandlebrot set are fun. Infinite detail with repeating patterns; almost like a cosmic secret is being revealed.

[@Lux_Absolute]

🦠

[@Deleted11100]

Cheers. I still haven’t got a clue. But I’m all for it. What time does it start?

[@balachandardevaraj496]

I think it's at 5pm today

[@Trevil666]

Been here for years, haven't learned any actual science but it is relaxing.

[@Tasorius]

Try watching a Mandelbrot zoom on KZbin 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...

[@Tasorius]

@@Trevil666 Looks like you are either ready to fall into the 4th dimension, or you are immune...

[@pelomyshadowsong3485]

You are my favorite kindergarten teacher. ❤

[@blufudgecrispyrice8528]

bro my mind would melt if she was my kindergarten teacher.

[@EllipticGeometry]

Kindergarten? I don’t think they covered fractals there, even superficially. But with the new new math, who knows.

[@Danbatio]

@@strawberrygoldie329 a while ago someone said her videos feels like the first day in a 4th dimension kindergarten.

[@johnlime1469]

​@@EllipticGeometryNew new kindergarten covers quantum physics, general relativity, bayesian statistics, and chaotic systems. The graduation project is developing cure for cancer.

[@frankconley7630]

Super pertinent for most people. Thank you. Explained so well.

[@emc3000]

I just like how it means almond bread

[@jordanmcgrory2171]

If you struggled with this, there's a song about this as well by Jonathan Coulton which may help.

[@BrontoByteStudio]

Tibees is the type of person to give us weekly math facts and still can make them entertaining😄

[@ottomondo1368]

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.

[@Jasper_4444]

That's interesting.

[@BillyMandalay]

The 'beetle' has always reminded me of some Crop Circles

[@vixeondaniels8886]

She's such a smart cookie! 👏 ❤

[@Deletirium]

I could listen to her voice for hours...

[@matrixtech6917]

Thank you for introducing me to this topic

[@Kristielina]

Thanks for the summary, it is nicely organized. ✨✨

[@apurvabaluni9]

Your explanation ❤

[@nicholascurran1734]

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!

[@9or10ofalltrades]

I feel like this represents the shape of the universe

[@seananthonyhart]

Nothing frames a pretty picture, and the ability for us to stand apart and watch together in the 4th Dimension.

[@McMissile00]

Hey Tibees, Just Wanted You To Know "If Beauty Was A Function, You'd Be An (e^x)ponential One..."

[@WereWade]

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

[@tommythecat4961]

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.

[@NormanChester882]

How amazing!!!

[@stefanmargraf7878]

As a kid of 13 i used my simple calculator to calculate the numbers of a Mandelbrot-Männchen and draw it on a paper.

[@cronoukie]

I never thought about this. Now that you mention it, it's cool

[@vocalbooth8585]

Your voice is amazing!

[@frangershwing]

Complex numbers are fascinating, they seem more "real" (more natural) than "real" numbers

[@stapler942]

Would you say then that rational numbers are more "natural" (integral) than natural numbers? 😉

[@frangershwing]

@@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.

[@stapler942]

@@frangershwing I'm being facetious by extending the pun space, don't mind me.

[@Tasorius]

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...

[@iamjmunroe]

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😅

[@Corusame]

I wonder if the Mandelbrot set could have some form of application in the real world.

[@rwm1980]

Its every where. Mandelbrot set is fractal math

[@thecrowsnest6963]

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.

[@tillybillyboyboy]

My favorite part of looking at the boundary is that it's the closest we'll get to glimpsing the infinitesimal 😗👌

[@msjkramey]

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

[@Leelz247]

This kind of looks like the phospholipid bilayer of the surface of a cell. May be a coincidence, bit wonder if there's a relationship. Anatomy does align with a lot of mathematical principles!

[@User-435ggrest]

I have watched those Mandelbrot zoom videos so many times, but never understood how it works😅

[@mrman5066]

This causes me such joy

[@wildfirefox1]

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 😂

[@jonaFUN999]

Arthur C Clarke made an excellent documentary on this called The Colors of Infinity with Mandelbrot himself

[@side2k]

Oh, nice to have you back. How was your trip into the 4th dimension?

[@anonxnor]

Interesting!

[@Renatus_Eruditus]

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 🌌

[@RupertBruce]

The thing that shows the set best is rotating the plot in 3d to show that's it's just a contour plot

[@duanemcclure8324]

2 words. SO COOL. 😁👍

[@smartervilleonroute66]

I could listen to you infinitely

[@joeldelabarrera1335]

Amazing explaining

[@jaredkaye3669]

I like to think about it in this format: -Zsub(n)^2 + Zsub(n+1) = C You are iterating in the i dimension. A.I. algorithms iterate in the i dimension as well. Consciousness is this.

[@Studiosagi]

The Mandelbrot Set is caked up

[@martinh972]

"Pathological monsters!"

[@MyHumanSuit]

This is my favorite thing.

[@Whom1337]

I wish my battery life was longer so I cold listen for hours

[@Mastermindyoung14]

Glaucus atlanticus reminds me of the Mandelbrot set

[@Nik-zf4xl]

My mind went to nyquist plots that I had studied in my past😊😊😊😊

[@mark_tilltill6664]

I like understanding you.

[@piyushlkhadgi]

Example shown is of a real number and she is saying complex number. Bit confusing to me.

[@jeanlawson9133]

She makes me think 🤔....🖤🌑🕶️🔥

[@edwardbanda6018]

Explain iterations and layering to complete the graph, pretty much all numbers much be plotted X, Y and sometime Z on a Cartesian coordinate system. to include all numbers, reals, rational, irrational, and imaginary.

[@coloneloxide]

Science aside, that voice is actually soothing

[@ronniemarshall7684]

her: "so about the mandelbrot set" me: *asmr induced coma*

[@Secretgeek2012]

I kind of get the iterative mathematical process. What I don't get is how that creates the fractal.

[@davidtriplett8105]

Proper analysis

[@iainmackenzieUK]

is there a simple link to chaos in this discussion?

[@markfaine2169]

U should upload more shorts like that

[@alexanderfreeman]

If you think that's interesting, just wait until you find out about the Mandelbrot set's connection to the logistic map!

[@gustavgustav5529]

I can see that. Thanks.

[@humanmonsters]

Can you talk about Julia sets please??

[@officermofiz4600]

I never thought I'd be happy to see some numbers being abducted to the Mandlebrot set but here we are... 😂

[@robinbrowne5419]

In biological terms the Mandelbrot set could be called Infinihairium or Bug with infinite hairs. (Here is its larvae 🐛 :-)

[@Skaevs]

You remind me of nearly all my math teachers who were women.

[@Greg_Rock]

Infinitessimal, defined.

[@KingLouisII]

Can't it also be said that squared decimal numbers also go to infinity? It's just a different kind of infinity, as the numbers get infinitely smaller.

[@elgracko]

The colors represent How Quickly they tend to infinity right? so, where's 0, 1, -1, i, -i?

[@questwithshahzad3058]

infinity is so mysterious what will those look like or think who live in infinity

[@danrazART]

Thanks. Now someone please explain this connection between finding such numbers and blockchain and ai art generators seeds?

[@paulgarcia8345]

Here’s the thing: the Mandelbrot Set is pure information, which means it couldn’t have evolved. How do you explain its origin then?

[@LakshayKakkar-fr4oi]

Please collab with jee simplified

[@user-jn4wt9pz7y]

what about 0 tho ? it stays the same no matter how many times you square it too !

[@tunazalad]

If its infinite then what happens if you zoom out? I haven't seen anyone zoom out on a fractal yet, on in.

[@jaimefairbanks5818]

The way you describe the process and the calculations don’t seem to match. How is 3squared plus one = 26?

[@shadowlife8368]

This is unrelated, but if the fourth dimension is time could there theoretically be a different 3 dimensions from ours? It would be the dimensions from 2 dimensions plus time.

[@SecularSynthesis]

Quanta explained this with much greater clarity

[@eatmyshorts8406]

is mandelbrot someone’s name or does it mean something different in english? because where i’m from that’s food(almond bread)

[@Vognar6]

It's name of the guy who invented/discovered it.

[@lewis7515]

​@@Vognar6 He didn't discover anything, he just marketed himself.

[@TheNoiseySpectator]

Well that is all well and good, but does it have any kind of application to the real world? Are there any circumstances when this "Mandelbrot pattern" would be manifested in nature?

[@thecrowsnest6963]

They're everywhere! Clouds, cauliflower, etc.

[@Kahneq]

Because all is one

[@gutharius]

But what type.of infinite complexity is it? What other types of infinite complexities are there?

[@ItsMeMissV369]

@tibees is an eye 👁 2D?

[@_WOR]

Now I’m convinced that when this lady isn’t making videos she’s watching Dragon Ball Z 😐.

[@TheMemesofDestruction]

Isn’t the Mandelbrot set bound by -2 and 2?

[@willjackson5885]

Not +2, but +.25

[@GoldenTiger01]

So dimensions are out and Mandelbrot sets are in?

[@kellyrobinson1780]

Wait. Hold the phone. Every time you do one of these iterations, you're squaring some number and then ADDING "1" to it. If every step adds "1", how do you NOT go to unfinity?? Luuucy? 'Splain this to me...

[@maverick_monkey]

Toby is using C=1 as an example of a complex number C which _isn’t_ part of the Mandelbrot set (because, as you rightfully explain, adding ones definitely leads us to infinity)!

[@onkar1202]

Lily

[@codatheseus5060]

Womandlebrot set

[@switzerlandful]

How does zero squared equal 1?

[@timeless_realm]

❤❤❤👸

[@Malangsufi]

What is the purpose of such set?

[@mattmathematics3591]

How do you apply this?

[@switzerlandful]

How can any number not lead to infinite or shrink infinitely?

[@switzerlandful]

As in, not do either, but is stuck intbetween?

[@switzerlandful]

Obviously 1 stays in between.