What's so special about the Mandelbrot Set? - Numberphile
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- Опубликовано: 17 апр 2019
- Featuring Ben Sparks discussing the Mandelbrot Set (and Julia Sets). Catch a more in-depth interview with Ben on our Numberphile Podcast: • The Happy Twin (with B...
More links & stuff in full description below ↓↓↓
More videos with Ben: bit.ly/Sparks_Playlist
Ben Sparks website: www.bensparks.co.uk
And on Twitter: / sparksmaths
Holly Krieger has done a few Mandelbrot videos on Numberphile...
The Mandelbrot Set: • The Mandelbrot Set - N...
63 and -7/4 are special: • 63 and -7/4 are specia...
Pi and the Mandelbrot Set: • Pi and the Mandelbrot ...
Fibonacci Numbers hidden in the Mandelbrot Set: • Fibonacci Numbers hidd...
Filled Julia Set: • Filled Julia Set
Ben was using Geogebra software: www.geogebra.org
Files from this video: www.geogebra.org/m/BUVhcRSv
Ben explains how he made the Geogebra files on his channel here: • Julia Sets and Orbits ... (part 1) and here: • Mandelbrot Orbits and ... (part 2)
He mentioned the book Chaos by James Gleick: amzn.to/2vj8ubP
Golden Spiral T-Shirt available in the Numberphile Teespring store: teespring.com/stores/numberphile
Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): bit.ly/MSRINumberphile
We are also supported by Science Sandbox, a Simons Foundation initiative dedicated to engaging everyone with the process of science. www.simonsfoundation.org/outr...
And support from Math For America - www.mathforamerica.org/
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Наука
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Catch a more in-depth interview with Ben on our Numberphile Podcast: ruclips.net/video/-tGni9ObJWk/видео.html
Love to see content creators still caring about 1 year old videos, keep it up :)
Re-watching these after listening to the podcast.
@@sparkycj9930 ''ס'ססד'דד'דס'דסס'דש'ססס'דס'דסדססדדס'ד'ססדס'דס'סססדסס''ססדס'סדדססד'ס'''ס'סד''סס-סס'דס''''ס''דס'ס'סס''''ס'דד'ססס'''ד''סססס'''ד''''ס''ס'ס'''ד'ס'ס'דס'ס''ס''''סס'''-ס'ס'ד'ד'ד''ס'סדד'ס''ד'ס''דד'דד''סס'סס'ס'דסס-סד'דסדד'ד'ס'ס'סד''''''ס''ד-דסדד'סדסס'דדסדססד'ד'''''דד''''ס'ּדסד'סדדסדסדדדסדס'סדסס''ססדסדסדסדדסססדסססדסססד'ס'ס'דס''דס''סד'דד'סּססדסדססדסדסדס'סדסדסססד'סד'''ססס'דסד''ד'ד'ד''דד'ד'ד'ד'סס'ס'ס'דסד'ס''ס'ד'סד'-ס''ס'סד'ס'דסדס''ד'דס'דד'ס'ד'ד''ּסּס'דסדסדדס'ס''ד'סס'ד'ס''סס'ס'סס'סד'ס'ד''סד'דס''ד'סס'ד''ד'סס''ס'ס'ד'ס''סס''ס'ד''ס''סד''ד''''ס'ד'ס'ד'ס'ס'ד'''ס'ס'ד''סס'ד''ד''''ס'ס'ס''ס'ס''ד''ס'ס'סד''ד''ס'ס'ס''ס'ס'ד'ד''ס''''ד''ד''סד'סד''ד'ס''ס'ד''ד'ד'ס''דס''דס'''ד'ד'ס'ד'סס'''''ס''ס'דס'ס''ס'ס'''''ס''''''ס'ססד'ס''ס'ססס'ד'ס'ס'סדס'סססס''ס'ס'ס''ס'ס'סדס'ססס''סס'''ס'ס'ס'דססדד'ס'ס''סס'ד'ססס'ס''ס''ס''ססדס''סדסד''ס'סדסדס'דססד'ס'דס'ס'ס'ס'ס'דס''סס'סס'ד'ס''דס'סס'סד'ס''ד'ססדסדסדסדססדס'סד'סדסּּ--ס----ד-ד'סדדדד'ס'ססדס-ד'סד'דדסדד'סדד--ד--ד'דּד'סדדדדד־-דדססד''ד'דססד'ד'דדסד'ד'ּּ-סדדדדדדדּ-דדד--דסדסדסדסדסד-ד'ד'ּּדּּסּדד-ססדס'דדּדדדד'דדּסד-דסד'דד-דדס'דד'דד''דסדד'ד'ד'ד''דדס''''ס''''ד''''ס'ד'דד'''סדד'סדס'ד'ד'ד'סס''דד'סס'ד''ד'ס'ס'ס''ס''ס'ד'דדש'ד'סד'ס'ד'ד'סס'ד'ססד'ס'סס'''ד'''ד'''ס''סד''ד'ס''דדסד'ס'ס'דסס''סססדס''ס''ס'''סד'''סס'ס'''ד'דדּדּדּ-דדדּדּּּּסדּדדדּּס1¹ס1ס1111ס1ס11ס1¹111ד'דדד111'ש1ש11ש1ש'ש'ש1ש
What computer program are they using to visualize this subject in the video? Very nice ^_^
Subtitles in spanish please
This is the first and only video i have ever seen trying to explain Mandelbrot set and actually succeeded.
Agreed!
Yeaah
Yup. Pictures > Words
Indeed.
not for me. Too complicated
Q: What does the “B.” In “Bernard B. Mandelbrot” stand for?
A: “Bernard B. Mandelbrot”
This comment is underrated
love your wit.
@@ricardosanchez2262 highly
Mandelbrot was legendary. Even the man’s name is a fractal!
I get it
I took a class in complex dynamics... the Mandelbrot set and Julia sets are some of the most comforting things I’ve seen in maths. They’re artifacts of logic, but they’re also things of beauty. It’s wonderful.
The scaling and rotating of space really is quite special isn't it
@@novygaming5713indeed
John 14:21
My head right now: Stable, unstable, stable stable, unstable
"The Mandelbrot Set is a geography of iterative stability" is my new catchphrase
The illustration of an algorithmic generation of a Mandelbrot set is akin to a topological map in which local structures resemble structures in equivalent Julia sets, connected through the concept of iterative stability
Catchy
New pickup phrase !
A new version of ''The mitochondria is the powerhouse of the cell''?
That was a really beautiful way of putting it, imo. Concise and poetic.
This was literally jaw-dropping. I'm almost brain-damaged when it comes to simple maths (tedious and boring to me), but the visualization here helped me to really appreciate what gets mathematicians high about their craft. It's poetry of the Gods...
You get the same results and even better when you do acid.
Lol.
That's what an acid trip is.
It opens your soul and mind to real life and the paradox in it.
Which means that we should feel relieved to know that we are gonna life again after we die, since it is a paradox, let's make better life choices.
@@alcirfigueroa3712 Lsd, dmt?
Alejandro Manuel Fernández Medina haha he doesn’t realize acid is trash XD
Alcir Figueroa hey mr lol, just saying lsd and acid is verrryyy different ( you don’t experience fractals on acid)
@Jack Volkwyn we’re kind of going off topic here, but acid is slang for lsd in different places. Don’t bash the man. As to the OP, I agree, this is mind blowing stuff. I think you’re on point with the poetry of the gods, the language of the gods.
OK, hands down this is THE BEST Mandelbrot Set video on all of youtube. It takes you from not even having to know math, to COMPLETELY understanding the Mandelbrot Set.
To be fair it's a pretty simple concept
When he zoomed in and then flipped over from the Mandelbrot pic to Julia set and then zoomed out again.. Amazing.
This isn't the video of a guy zooming in on the Mandelbrot we need. It's the one we deserve.
Top comment after over a year doesn't even have a single reply, and that's because it does not need one. It is perfect as is.
@@soupisfornoobs4081 you ruined perfection.
@@cman7609 so did you, and i as well lolol. Honestly tho this is the first video that actually explains mandelbrot that the average joe can understand
When someone use a T-shirt as a video background, he is definitly a reputable mathematician!
20 years of caring about it, and I finally “get” the Mandelbrot Set.
Thank you.
What's your arbitrary rules for 'getting' it? It shouldn't have taken so long to understand what the image represents. And it'll take you infinitely forever to truly understand what you're seeing.
@@gamefreak113456 you're so negative ugh
@Long duk dong stop being so negative
you get it when you can program it
@@gamefreak113456 What SHOULD have taken so long is finding the video that explains what the image represents
13:05 “I don’t think RUclips needs *more* videos zooming in on the Mandelbrot Set”
No disrespect sir, but not only does RUclips need more Mandelbrot Set zoom ins,
It needs more of *YOUR* zoom ins
Agreed, it doesn't need any more low quality videos set to crappy music, it needs more videos with a guy piloting who knows where he's going, and is great at explaining abstract concepts.
I believe they use it in video games , films etc.
Found the acid users
Better Mandelbrot than kittens.
@@laurakeyse9944 they use fractals in games?
Thank you for this explanation. It ‘clicked’ for me around 14:52 - realizing the infinite nature is because you can get infinitely closer to any point in the set without ever arriving to it - but it’s still a ‘real’ set of numbers that exhibit a geography based on stability. Awesome.
The name for the phenomena you just describes is called Asymptotes.
Every point on the set can be arrived at by travelling along other points that are on the set. It's completely connected. Watch some zoom videos and keep that in mind. It's... insanity.
can i have a loop of him saying "stable, unstable". It was oddly calming.
Best ringtone
Mandelbrot ASMR
time stamp plz
@@Malmorious 5:15 12:15
1:46
This is brilliant. One of the best explanations of what's happening in both sets that I've seen. Thanks Ben!
Red Dunkey no one cares no one asked
np
what's crazy is that fractals are basically all I see when doing LSD, at least with peak visuals
It's like he uncovered the key to mathematically understanding the build of the universe.
Man, this seems so incredibly complicated, but when you get to visualize it, it's definitely not...
Now I take my hat off for those mathematicians who researched all of these crazy things without being able to visualize it as clearly as we do now.
visual language is the future
@@nottoday3878 it's how the brain evolved in the environment on earth. Visual language isn't the future it's the past
They were on shrooms, so don't worry...
@@Wolffanghurricane I will add spice to the topic.
Time has no direction - past, present and future are only happening in our heads. We record data of reality as it constantly changes. What data we have about it defines the past, and the predictability of the system’s effects defines the future. But really, time isn’t like this so your statement is simply wrong. Visual communication isn’t past nor future, it’s present and will always stay like that, it’ll only change (evolve).
The golden teacher shrooms teached me the mandelbrot 😂
So, I've had the Mandelbrot set as my profile picture on here for nearly a decade and this is THE best video describing what the image actually means. Thanks, Numberphile! This was awesome. Kind of blew my mind a bit, too, so much so that I had to pause the video at around the 6-7 minute mark and check out the Geogebra links in the description to play around with it myself.
actually same
STILL mindblowing.
Zooming into the Mandelbrot Set:
*_How it feels to chew 5 gum_*
3 months ago I was addicted to watching Mandelbrot set zooms, I was 3 months sober, then he started zooming and I was like "Not again!".
@@nonamehere1626 Oh no, I bet now you can't stop!
5+i Gum
Stimulate your chaos..
Mr WhiteHawk Stimulate your imagination
Chaos theory: A small change that explodes into uncertainty.
May be 🦋 effect.
I can barely do simple math but this was explained in such a digestible way, I really understand what mathematicians see in their work.
Seeing those animated zoom-ins makes it a lot more obvious why some people call the Mandelbrot Set "God's Fingerprint."
Math = nature.
@@rocren6246 /\ This! /\
@@rocren6246 if nature created itself alone wouldnt be chaotic instead orderly
@@rocren6246 lol no my friend. Math does not = nature. What is nature made of?
@@loganwillett2835 I was told long ago (I think it was an algebra teacher??) that "Think of Math as a language, instead of bunch of numbers"....Now I see why
This is one of my favorite Numberphile videos ever. I've probably seen 90% of them but this tops them.
My previous favorite was Epic Circles but this one goes way beyond that even. Definitely the best Numberphile video to date for me personally.
Me too!
I came here to say that, feels great that im not the only one. I can feel the passion with which he talks about this!
Agreed!
And the golden ratio one...
The fact that Julia and Mandelbrot had no modern computers made them use the only tool they had available, their imagination. That's how you come up with revolutionary ideas.
This was one of the best videos I have seen on the subject and for the first time I can say that I understand what's going on.
"You can programme it in 10 seconds on a spreadsheet." Yeah, it took me a morning
Share the file
Now that you know how to do it, do it again and make a spreadsheet about your progress on speed. Assuming you can improve your time every single time you reprogram it, you get your own little James Moreland set :) The beauty of repetition and recursion. It's something everybody should appreciate in my opinion - people improve.
I would be there a lifetime... I cant even get simple math in excel.
You should publish that geogebra file, if it's not available already.
you can just google it "mandelbrot set geogebra" theres a few with similar results
Go to the description ^^
One of THE best videos of Numberphile
vSpecky I agree! Think this is my new fave!
up there with the regular polytopes one.
Fabulous... Thank You !!!
In 1988, using a 386 based Windows PC, I built many Mandelbrot and Julia sets, one pixel at a time, and each image took a day or two to complete. Now, with processor speeds in the gigahertz and multicore processors working in parallel, each image takes milliseconds to complete. Was very interesting to watch the machine back then do the calculations and plot the pixels on the screen. Now, all the math is done in a flash. Shows how far we have come in technology. Still love the Mandelbrot images. They are seen everywhere in nature.
I think this is one of the best videos of numberphile. The world needs more teachers like Ben. Thanks!
I knew Brady would say "It blows up" instead of "It diverges"
"Kaboom" for diverging, "plop" for converging on a fixed point, "beep-boop" for converging on a group of fixed points.
"blows up" is less technical but maybe more descriptive
@@hymnsfordisco especially for people less interested in maths who may not know what convergence and divergence is
goes toward infinity.
He does it so people can understand
10:56 That book! I've been trying to remember it's name and author for 20 years! At Last! I can go read it again! Thanks for mentioning it!
I've been fascinated by this stuff for thirty years, and this is the first time someone could explain it to me in a way I could actually understand. Thank you so much!
Absolutely outstanding video. Thanks! I have loved the Mandelbrot set for years without properly understanding what it is. In the last two days I've been looking at clips about how it's made and these NumberPhile videos are brilliant. The programmes you use to show the patterns within the '2' boundary are amazingly helpful at showing the patterns.
I'm gonna zoom anyway because it's a whole new adventure everytime!
I would like to see that in a video, someone programming the Mandelbrot Set in a spreadsheet in 10 minutes
Me too !!!! I want that program code !
*seconds
Sounds like a job for non other than Matt Parker!
@@qbaker20 i bet if Matt does it, it will become a Parker Set ;D
Lol
I've always been fascinated by the huge length Mandelbrot zoom videos and this actually explained it really well. Glad this was recommended to me. Great video.
This is the most incredible explanation I've seen of the Mandlebrot set. I see it, and I understand it!
This is the single best explanation of the Mandelbrot set I've ever seen. Please do more, or better yet an entire series, using this software!
Ben’s passion for teaching is incredible. What a man!
Watching this again. Ben is one of the clearest explainers of complex concepts on Numberphile.
This is a brilliant introductory description of these sets. Thank you.
The universe implodes.
This is the clearest explanation of the Mandelbrot and Juliet sets ever
“it’s a geography of iterative stability” nice
This is real mathematican's glory.Because any shape that is on the line just foreverly keeps going and going.It's beautiful
I read Chaos about 16 yrs ago. It really effected how I think about a lot of things.
Required reading.
"Death to the False Emperor! Death to the weakling Imperium of Mankind!"
einyen1
What does that mean?
@Larry Scott Yeah, I read it in the mid 90's, it has shaped my thoughts in many ways ever since. I'm actually looking forward to re-reading it, I lost my copy and couldn't remember the name correctly.
@@Einyen This does not come from Mankind! Glory to the true Kingdom!
@@larryscott3982 You did not specify which Chaos you were talking about, so I just decided it was Chaos Space Marines...
That julia set ~ mandelbrot mapping is absolutely bonkers damn
One way to think about it would be as slices through a 4D space of (z0r, z0i, cr, ci), with the usual view of the Mandelbrot set being the slice (0,0,cr,ci).
A 4D Mandel/Julia hypervolume explorer might be an interesting little programming project.
+Roxor128 Now we’re talking... damn, that would be amazing
One of the most well-done videos. Beautiful and insightful.
The enthusiasm is infectious! Thank you for this channel. :)
I've been looking at this stuff for decades and read several books on it, you finally and very lucidly explained it, thank you very much!
I have watched every Numberphile video ever posted and I believe that this is the best. Extraordinary clarity and very well constructed. Well done indeed.
It is amazing how you ask the perfect questions in between the explanation.
This was the best explanation and demonstration ever. Other videos just talk about the discovery and showing pics, but never really demonstrated it like this. This blew me away!! Thank you for this video!
So this finally makes the link between chaos and fractals clear, nice work.
This was a truly wonderful video. One of the best Numberphile has ever done, and one of the best on Mandelbrot, and also one of the best ever on simplifying things to its essential. It's hard for a mathematician to imagine talking about Mandelbrot without talking about complex numbers. Ben here said forget about complex numbers. This was really great.
This is the best, clearest and most beautiful explanation of Mandelbrot that I have ever seen. Thank you
This is by far one of the better explanations of Mandelbrot on youtube. Thanks for the great videos Numberphile!
1:48 I almost feel like crying. Thank you so much! That makes it all so clear!
Kind of off topic comment... besides the absolute amazingness of this video and the Julia and Mandlebrot sets, I would like to say that another redeeming feature of this video are its comments. Numberphile fans are all so positive and generally non-troll like. That is so refreshing on RUclips and social media generally. Everyone, keep up the fantastic work!
Agreed!
This aged well. Much love my friend !
Speaking as an actual troll, living beneath a bridge in darkest Cornwall, I find your comment offensive. We have feelings too.
Such complexity from such simplicity. Blows my mind every time.
I love this video! it boggles my mind to think this was figured out without advanced visualization tools. the mandelbrot set is a beautiful testament to the importance of curiosity and experimentation
Crazy how the more you understand it the more you are fascinated by it. Probably the best Mandelbrot Set video on this channel :)
The diagram is on a brown paper background
More sustainable ;)
It's mind boggling to think this trippy chaotic/stable shape makes perfect sense and has much more meaning than just a cool screensaver! I am so grateful that he explained it in such fine detail. Thank you Numberphile!!!
I'm a total layman here. I can now almost understand the Mandelbrot Set. Love it. Great job. Thank you.
The software used at the end is XaoS and it's available for free
Thanks!
When someone use a T-shirt as a video background, he is definitly a reputable mathematician!
Two years later and you are still a hero
Possibly a slip of the tongue is made around 1:46 when "stable, stable, unstable ..." is being addressed in the opposite way to 2:00.
ShortLessonsHardQuestions yes it was that. The ones that point to zero are “stable”
He did that in an unstable fashion.
thanks :D
Yeah, it seemed a bit unhinged. Perhaps the video is out of sync, but I don't expect an unglued video from Numberphile.
This is why I stick to books when learning math. People explaining things in real time are so unstable.
Absolutely astounding.. Thank you for presenting this in a way I can understand. Has always intrigued me, but never been able to get my head around it. Well done.
Man, the theories that come to mind relating to the universe when implicating the complexity of this
When someone use a T-shirt as a video background, he is definitly a reputable mathematician!
We live in a simulation.
Wow, Ben is a fantastic communicator! Well done!
Ben's videos are genuinely the most interesting and mind-blowing Numberphile content.
bro i fell in love with the way u teach mathematics, it must be truly inspiring to watch one of ur classes personally
Congratulations, this video has earned a space on my “best videos possible” playlist. 🥳
This is your best video to date! I actually understand this and can code it from memory of this video.
Thank you very much for this.
Amazing video with wonderfully clear explanations. Thank you so much!
Marvelous explanation of how the Mandelbrot Set came together. If would have to see this explained probably a few times to really begin to understand it.
Awesome video..!
I first heard of the Mandelbrot set when in design school and never made any sense why that shape was always appearing. With this explanation every detail is explained and never got lost on intricate descriptions....but the best part about this presentation is Hollies voice and pictures sprinkled sparingly throughout the video.
First time I actually understood the set ! Absolutely amazing video. Congrats to both.
I’m not a math nerd but this is fascinating and also makes beautiful art!
This is by far one of my favourites videos from youtube!
When i programmed a Julia/Mandelbrot Set visualization/exploration program as an assignment the moment where i got the calculations right and the resolution high, and the beautiful shape popped up was so satisfying. Truly amazing piece of mathematics.
I've been a mathemetician for over ten years now and finally I understand this. thank you
Really weird question: I find math kinda cool and if I was better in it wouldn't mind making it a career... but what sorts of jobs exists for mathematicians? I don't mean this in a rude way, I'm genuinely curious.
@@DailyCakeSlice for the most part you get paid to teach maths to others. despite its wide applications, the study and discovery of mathematics is a relatively narrow field. That said, there are plenty of jobs within that narrow field available. Plenty of schools ranging from beginning grade school all the way up to university need passionate mathemeticians to teach maths to their young students. Some professors make quite a lot of money studying their passion, and since passion is what drives both teaching and learning, that's the best career for anyone who loves maths.
@@DailyCakeSlice Apply for a job at Jane Street
@@DailyCakeSlice Math is needed in almost all fields of computer science. As a game developer you need quite a bit of math. Of course it always depends on what you want to do. However understanding vectors, matrices and quaternions is quite important if you do 3d graphics. In the game industry there are even other jobs like game design which is more about probability and balancing features. They usually toy around a lot with exponentials ^^.
Though it depends on how deep you dive into certain topics. Procedural geometry or neural networks are also quite math heavy. Same goes for bezier curves or splines.
Realistically speaking in almost all fields there are jobs that require some level of math. Yes, the requirement of a pure mathematician is kinda rare, but math skills are required everywhere ^^.
A useful numbering system for briefcases on Deal Or No Deal hosted by Howie Mandelbrot.
The joke doesn't work quite as well in the UK, where it was hosted by Noel Edmonds - and no-one wants an iteration of him, or Mr. Blobby
I thought you were making a Brexit joke for a minute. Now there's an example of iterative instability. :-)
Fantastic video! Very well explained and yet does not take away from the intense mindboggling experience i have with this.
That image at 15:00 is beautiful, and it's really cool to think someone led us to this without the tools to visualise this as well as we can now.
ive been obsessed with fractals and the mandlebrot set from the moment i saw them... my jaw was dropped this WHOLE video and i barely understand it, yet it makes so much sense! thank you thank you! i LOVE this video!
Glad you liked it.
Thanks for mentioning James Gleich's "Chaos" :) Been ages since I read it, had almost forgotten about it, but along with the appendixes to Arthur C. Clarke's "The Ghost from the Grand Banks" (which is science fiction but involves fractals), it gave me the first inkling of understanding what fractals are and how they work. Thanks to you it's now safely in store on my Kindle :D
This video is remarkably one of the most best videos on Mandelbrot Set👍👍
This was just beautiful. Thank you for sharing the geogebra files! I am going to use this with my students.
Well done! Well done video. Seriously. This made my day. Looking for vids on the Mandelbrot Set and ... this nailed it. Thanks!
Best explanation of the Julia and Mandelbrot sets I've ever watched! Thank you :D
Here’s an interesting idea:
“To claim to know everything about something is like claiming to be able to draw the Mandelbrot set”
Yeah but do you _know_ this idea is actually interesting?
@@unvergebeneid which iteration of stable knowledge indeed
I must try this out on some of my know it all acquaintances.
It's always surprising how that simple formula can generate such a beautiful mathematical monster 🙂
Many of our plants and animals have features that are mathematical. There is a fractal that produces a fern, for example.
agreed. Im totally blown away by the contrast between chaos and predictability in those images. It's truly beautiful.
This is the most amazing thing I have ever seen. Like literally.
The best explanation of the Mandelbrot set I think I've ever seen!
I think the other video did a fine job explaining the phenomenon, but this one gave a nice live visual outlook on it!
I'm not mathematical but I'm obsessed with this.
But this is “mathematical” inherently... I’m struggling to make any sense of your comment, it seems contradictory.
this, gives me goosebumps and i don’t know why.
Amazing how something complex was explained so clearly!
best video I've seen this year
This was such an amazing video. I now understand what the Mandelbrot set is and why people were making a fuss over it. I never saw a journalist explain what it was exactly. So cool!!!!