So what is the Mandelbrot set anyway?

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  • เผยแพร่เมื่อ 9 ก.พ. 2025

ความคิดเห็น • 314

  • @Andrews__YT
    @Andrews__YT ปีที่แล้ว +1807

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

    • @lewis7515
      @lewis7515 ปีที่แล้ว +58

      It's painful.

    • @robocombo
      @robocombo ปีที่แล้ว +123

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

    • @thecringequeen31
      @thecringequeen31 ปีที่แล้ว +123

      @@robocomboBenoit B Mandelbrot

    • @FirstSynapse
      @FirstSynapse 11 หลายเดือนก่อน +41

      So this is what a Mandelbrot set actually is

    • @moodonut
      @moodonut 11 หลายเดือนก่อน +24

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

  • @Keradurakh
    @Keradurakh ปีที่แล้ว +861

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

    • @ricardolobos673
      @ricardolobos673 ปีที่แล้ว +17

      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
      @lewis7515 ปีที่แล้ว +7

      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
      @nickcara97 ปีที่แล้ว +40

      @@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
      @Bassotronics ปีที่แล้ว +2

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

    • @andhewonders
      @andhewonders ปีที่แล้ว +13

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

  • @niravelniflheim1858
    @niravelniflheim1858 11 หลายเดือนก่อน +132

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

    • @Lux_Absolute
      @Lux_Absolute 11 หลายเดือนก่อน +2

      🦠

    • @christina_kaur
      @christina_kaur 2 หลายเดือนก่อน +1

      Math is the language of the universe 😊

    • @AkinatorKing-37
      @AkinatorKing-37 หลายเดือนก่อน

      🧑🏾‍🚀.

  • @bryangreen6231
    @bryangreen6231 ปีที่แล้ว +346

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

    • @KJKP
      @KJKP 10 หลายเดือนก่อน +1

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

    • @Tasorius
      @Tasorius 7 หลายเดือนก่อน +7

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

    • @Tasorius
      @Tasorius 7 หลายเดือนก่อน +8

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

    • @Player_is_I
      @Player_is_I 4 หลายเดือนก่อน +1

      Thought I was alone

    • @lilpetz500
      @lilpetz500 3 หลายเดือนก่อน +3

      ​@@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

  • @dubistverrueckt
    @dubistverrueckt ปีที่แล้ว +91

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

  • @BleuSquid
    @BleuSquid ปีที่แล้ว +117

    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
      @sheep1ewe ปีที่แล้ว +4

      Thank You for the explanation!

    • @thecrowsnest6963
      @thecrowsnest6963 ปีที่แล้ว +2

      Very nice! Thank you!

    • @johnlime1469
      @johnlime1469 10 หลายเดือนก่อน +1

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

  • @murphybed7919
    @murphybed7919 ปีที่แล้ว +38

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

  • @seawright2307
    @seawright2307 3 หลายเดือนก่อน +25

    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🎵🎶🎵

  • @zeruzio1345
    @zeruzio1345 ปีที่แล้ว +99

    Tibees + 3blue1brown collab when?

    • @gdclemo
      @gdclemo 4 หลายเดือนก่อน +2

      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...

  • @KI4ASK
    @KI4ASK 3 หลายเดือนก่อน +1

    One of the most straightforward explanations of the Mandelbrot set I’ve ever heard. Thanks!

  • @frankconley7630
    @frankconley7630 11 หลายเดือนก่อน +3

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

  • @leyvua7362
    @leyvua7362 3 หลายเดือนก่อน +1

    This is so helpful and interesting. Too much that I shared it with aeronautical engineering colleagues group chat. Virtual hugz from Mexico 🇲🇽

  • @peterlustig7336
    @peterlustig7336 3 หลายเดือนก่อน +2

    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

  • @emc3000
    @emc3000 ปีที่แล้ว +7

    I just like how it means almond bread

  • @madbrowndog4887
    @madbrowndog4887 หลายเดือนก่อน

    I didn't understand a word of that, but I feel so calm and relaxed now!

  • @pelomyshadowsong3485
    @pelomyshadowsong3485 ปีที่แล้ว +36

    You are my favorite kindergarten teacher. ❤

    • @blufudgecrispyrice8528
      @blufudgecrispyrice8528 ปีที่แล้ว +10

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

    • @EllipticGeometry
      @EllipticGeometry ปีที่แล้ว +7

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

    • @Danbatio
      @Danbatio ปีที่แล้ว +8

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

    • @johnlime1469
      @johnlime1469 10 หลายเดือนก่อน

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

  • @BrontoByteStudio
    @BrontoByteStudio ปีที่แล้ว +23

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

  • @BillyMandalay
    @BillyMandalay ปีที่แล้ว +6

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

  • @Deleted11100
    @Deleted11100 ปีที่แล้ว +68

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

    • @balachandardevaraj496
      @balachandardevaraj496 11 หลายเดือนก่อน +1

      I think it's at 5pm today

    • @Trevil666
      @Trevil666 8 หลายเดือนก่อน +1

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

    • @Tasorius
      @Tasorius 7 หลายเดือนก่อน +2

      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...

    • @Tasorius
      @Tasorius 7 หลายเดือนก่อน

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

  • @Kristielina
    @Kristielina 10 หลายเดือนก่อน +1

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

  • @Deletirium
    @Deletirium 6 หลายเดือนก่อน +1

    I could listen to her voice for hours...

  • @9or10ofalltrades
    @9or10ofalltrades ปีที่แล้ว +1

    I feel like this represents the shape of the universe

  • @vixeondaniels8886
    @vixeondaniels8886 11 หลายเดือนก่อน +9

    She's such a smart cookie! 👏 ❤

  • @Billy_the_Greek
    @Billy_the_Greek 2 วันที่ผ่านมา

    I really enjoyed your guest season on Jet Lag! You were brilliant!

  • @charldew
    @charldew 3 หลายเดือนก่อน

    I finally get it! Thank you for a very clear and succint explanation.

  • @amitabhjayaswal
    @amitabhjayaswal 3 หลายเดือนก่อน

    Neat and elegant! Thanks Tibee!

  • @campfireeverything
    @campfireeverything 3 หลายเดือนก่อน

    This is my favourite ASMR channel.

  • @seananthonyhart
    @seananthonyhart ปีที่แล้ว +1

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

  • @matrixtech6917
    @matrixtech6917 ปีที่แล้ว +1

    Thank you for introducing me to this topic

  • @INVGProductions
    @INVGProductions 3 หลายเดือนก่อน +1

    I find that understanding the Mandelbrot set starts with understanding the Mandelbrot set.

    • @JanWnogu
      @JanWnogu 3 หลายเดือนก่อน +1

      To understand recursion you need to understand recursion 🤣🤣🤣

  • @Tommidgely170
    @Tommidgely170 3 หลายเดือนก่อน

    Thanks for that important detail. I never realised this.

  • @kurogane2638
    @kurogane2638 3 หลายเดือนก่อน +1

    Oh its the nice math lady that does shorts that send me sprialing into existential terror

  • @nicholascurran1734
    @nicholascurran1734 ปีที่แล้ว +2

    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!

  • @rayrocher6887
    @rayrocher6887 4 หลายเดือนก่อน

    Excellent work, thanks

  • @jordanmcgrory2171
    @jordanmcgrory2171 ปีที่แล้ว +4

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

  • @WereWade
    @WereWade 11 หลายเดือนก่อน

    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

  • @cronoukie
    @cronoukie ปีที่แล้ว

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

  • @vocalbooth8585
    @vocalbooth8585 11 หลายเดือนก่อน

    Your voice is amazing!

  • @wildfirefox1
    @wildfirefox1 11 หลายเดือนก่อน

    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 😂

  • @Tasorius
    @Tasorius 7 หลายเดือนก่อน +1

    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...

    • @steelhurricane4041
      @steelhurricane4041 25 วันที่ผ่านมา

      One guy says it's proof that God exists.

  • @frangershwing
    @frangershwing ปีที่แล้ว +10

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

    • @stapler942
      @stapler942 11 หลายเดือนก่อน +1

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

    • @frangershwing
      @frangershwing 11 หลายเดือนก่อน +1

      @@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
      @stapler942 11 หลายเดือนก่อน

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

  • @MuthuKumaran-hb6ku
    @MuthuKumaran-hb6ku 3 หลายเดือนก่อน

    Thank you Toby!

  • @Brambrew
    @Brambrew 4 หลายเดือนก่อน +1

    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.

  • @apurvabaluni9
    @apurvabaluni9 7 หลายเดือนก่อน

    Your explanation ❤

  • @NormanChester882
    @NormanChester882 ปีที่แล้ว +1

    How amazing!!!

  • @zapfanzapfan
    @zapfanzapfan 3 หลายเดือนก่อน

    Staring into the infinity of your eyes... oh, the Mandelbrot set is nice too...

  • @markfinn825
    @markfinn825 3 หลายเดือนก่อน

    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.

  • @smartervilleonroute66
    @smartervilleonroute66 11 หลายเดือนก่อน

    I could listen to you infinitely

  • @ADITYAK0TKAR-l6f
    @ADITYAK0TKAR-l6f หลายเดือนก่อน

    By the way,
    How can you keep a smile on your face forever?
    Your smile is cutest one 😊

  • @ShanBojack
    @ShanBojack 4 หลายเดือนก่อน

    Maths ASMR ❤ her voice is just 🙌

  • @topquark22
    @topquark22 3 หลายเดือนก่อน

    The Mandelbrot set was actually what piqued my interest in mathematics. I studied extensively, and wrote several software to plot it.

  • @mrman5066
    @mrman5066 11 หลายเดือนก่อน

    This causes me such joy

  • @carlosacevedo6009
    @carlosacevedo6009 3 หลายเดือนก่อน +1

    ASMR Science. Thank you.

  • @tillybillyboyboy
    @tillybillyboyboy 11 หลายเดือนก่อน

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

  • @Nik-zf4xl
    @Nik-zf4xl 11 หลายเดือนก่อน +2

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

  • @stefanmargraf7878
    @stefanmargraf7878 11 หลายเดือนก่อน

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

  • @Studiosagi
    @Studiosagi 9 หลายเดือนก่อน

    The Mandelbrot Set is caked up

  • @joeldelabarrera1335
    @joeldelabarrera1335 11 หลายเดือนก่อน

    Amazing explaining

  • @tommythecat4961
    @tommythecat4961 11 หลายเดือนก่อน

    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.

  • @MuthuKumaran-hb6ku
    @MuthuKumaran-hb6ku 3 หลายเดือนก่อน +3

    But u r adding it to 1 in the video..

  • @MyHumanSuit
    @MyHumanSuit ปีที่แล้ว

    This is my favorite thing.

  • @msjkramey
    @msjkramey 11 หลายเดือนก่อน

    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

  • @goyboysoy
    @goyboysoy 11 หลายเดือนก่อน

    Science aside, that voice is actually soothing

  • @ronniemarshall7684
    @ronniemarshall7684 11 หลายเดือนก่อน

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

  • @unclerat2131
    @unclerat2131 3 หลายเดือนก่อน

    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.

  • @ottomondo1368
    @ottomondo1368 ปีที่แล้ว +6

    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
      @Jasper_4444 ปีที่แล้ว +2

      That's interesting.

  • @User-435ggrest
    @User-435ggrest 11 หลายเดือนก่อน

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

  • @jetzeschaafsma1211
    @jetzeschaafsma1211 3 หลายเดือนก่อน

    If I wanted to listen to an ASMR voice, I probably would have googled that.

  • @officermofiz4600
    @officermofiz4600 ปีที่แล้ว

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

  • @vj.joseph
    @vj.joseph 3 หลายเดือนก่อน +1

    Where were you,when I was learning math?❤

  • @andrewbreding593
    @andrewbreding593 3 หลายเดือนก่อน

    The only rule for existing is don't be the set that destroys it's relevance

  • @davidtriplett8105
    @davidtriplett8105 ปีที่แล้ว

    Proper analysis

  • @Kahneq
    @Kahneq 8 หลายเดือนก่อน

    Because all is one

  • @iamjmunroe
    @iamjmunroe 7 หลายเดือนก่อน

    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😅

  • @robosing225
    @robosing225 3 หลายเดือนก่อน

    Her voice sounds like soft wind chimes.

  • @Hi_Brien
    @Hi_Brien หลายเดือนก่อน

    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)

  • @Corusame
    @Corusame ปีที่แล้ว +5

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

    • @rwm1980
      @rwm1980 ปีที่แล้ว +2

      Its every where. Mandelbrot set is fractal math

    • @thecrowsnest6963
      @thecrowsnest6963 ปีที่แล้ว

      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.

  • @Ed19601
    @Ed19601 3 หลายเดือนก่อน

    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

  • @mark_tilltill6664
    @mark_tilltill6664 ปีที่แล้ว

    I like understanding you.

  • @Ayoub97-97
    @Ayoub97-97 5 หลายเดือนก่อน

    Thank you

  • @joshuatillman60
    @joshuatillman60 2 หลายเดือนก่อน

    Amazing content. Happy to subscribe for more 😊

  • @iheardthat1b4
    @iheardthat1b4 3 หลายเดือนก่อน

    Mandelbrot! Mandelbrot! Mandelbrot!

    • @bleanG
      @bleanG 3 หลายเดือนก่อน

      Almond bread xd or is it a bakery item idk

    • @iheardthat1b4
      @iheardthat1b4 3 หลายเดือนก่อน

      @bleanG I guess there aren't many Seinfeld fans here. 🤣 🤣 🤣

    • @bleanG
      @bleanG 3 หลายเดือนก่อน

      @@iheardthat1b4 yeah lol

  • @Samu_Samu4
    @Samu_Samu4 หลายเดือนก่อน

    The German word Mandelbrot translates to almond bread

  • @RupertBruce
    @RupertBruce ปีที่แล้ว

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

  • @anonxnor
    @anonxnor ปีที่แล้ว +4

    Interesting!

  • @Whom1337
    @Whom1337 11 หลายเดือนก่อน

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

  • @Strange_Armour
    @Strange_Armour หลายเดือนก่อน

    When are you gonna be a guest on Countdown? 😍😍😍😍😍

  • @martinh972
    @martinh972 11 หลายเดือนก่อน

    "Pathological monsters!"

  • @jonaFUN999
    @jonaFUN999 ปีที่แล้ว

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

  • @McMissile00
    @McMissile00 9 หลายเดือนก่อน +2

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

  • @duanemcclure8324
    @duanemcclure8324 7 หลายเดือนก่อน

    2 words. SO COOL. 😁👍

  • @Renatus_Eruditus
    @Renatus_Eruditus 9 หลายเดือนก่อน

    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 🌌

  • @d69p-eix
    @d69p-eix หลายเดือนก่อน

    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

  • @ewg6200
    @ewg6200 3 หลายเดือนก่อน

    Numbers less than one BUT GREATER THAN -1 get smaller when you square them

  • @hesido
    @hesido 3 หลายเดือนก่อน

    Do you have an audio book because I can listen to this voice forever.

  • @pi_xi
    @pi_xi หลายเดือนก่อน

    -2 is smaller than 1 and gets larger, not smaller, when you square it.

  • @y4lnux
    @y4lnux 3 หลายเดือนก่อน

    By the way Benoit autobiography is great... Is an amazing story of survival and unconformity... The Fractalist

  • @gustavgustav5529
    @gustavgustav5529 ปีที่แล้ว

    I can see that. Thanks.

  • @simondalton3726
    @simondalton3726 3 หลายเดือนก่อน

    It’s known as the finger print of god. It’s found everywhere in nature.

  • @jeanlawson9133
    @jeanlawson9133 7 หลายเดือนก่อน

    She makes me think 🤔....🖤🌑🕶️🔥