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.
@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.
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.
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.
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.
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
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.
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.
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.
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.
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.
Wow. That's what I call some exceptionally well spent 16mins 52secs together with my son. Me: 50+ remembering when my high school suddenly decided to hop on the PC trend that was raging at the time. They splurged on a new computer lab, crammed with 386:s and even the occasional 486 PCs. You had to run to get a seat at one of those super fast ones after school. They would render this new strange computer-math thing they called 'fractals' faster, with more colours. (also Test Drive would run smoother). Mesmerized and frustrated. The impatient feeling of just almost understanding. Him: 14, like me tired in the morning, like me always late for school. Always liked math, his favourite subject. Oh joy. The sparkle in his eyes watching this! Patient too, stopping the video to explain when I didn't follow. Both laughing, minds blewn and then blewn again. Thanks!
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.
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.
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!
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!
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.
@@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
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.
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.
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.
@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.
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!
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
Have you heard of the angry cousin of the Mandelbrot set, called 'the burning ship' Fractal It has French gothic towers, and its spires are more french gothic towers And those are technically the chaotic regions that aren't part of the set. It's a real brain bender
I read about this years ago, kinda understood the basics but it was so vague, than this video actually shows you from the beginning and how they came up with that. I can say i understand it better now, this video rocks
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.
@@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).
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!
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 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 ^^.
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.
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.
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.
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
What a brilliant brilliant video!!!! 😍 I was also delighted to know that Mandelbrot was alive until recently. Gladly, when I was studying and coding. We used to plot Mandelbrot sets in Python and trip on them. 😄
5:14 It's happening fast, but it seems the instability happens when any 3 points leave the circle. When the 3rd point touches the circle, it becomes unstable.
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!!!!
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.
He mentions the book Chaos by James Gleick and that is how I found this video because I am reading it now and wanted to understand more about the Mandelbrot set. Thanks
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.
You mentioned that you know a number is going to explode when the absolute value is greater than 2. I recently found out that the general formula for the best possible escape radius is 2^(1/(n-1)) where n is the power in the iterative formula. For the Mandelbrot set that's z -> z^2 + c so n=2 which indeed yields 2, but for other powers it's a different number.
absolutley insane video, i had a really mad experience on laughing gas where i passed out and saw part of the mandelbrot set zooming in as time slowed massively and i could predict my own thoughts as they were coming to me in real time but my perception was slowed i was aware of fractals and their significance but never watched a video about them or saw a zoom in. was shocked to my core when i finaly watched one a while back and this has done it again
Great explanation video... even I, a total non-mathematician, could get at least an inkling of how these seemingly magic (and mesmerizing) fractals function.
I've always known the Mandelbrot Set as "some sort of fractal pattern"... Thank you for making sense of it for me in a visual way that was both stimulating and strangely calming... Thank you. =)
![Blox Fruits Dragon Rework Update [Full Stream]](http://i.ytimg.com/vi/EqDAp8udhm0/mqdefault.jpg)
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.
@@TheRealKinetic-q1t ''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
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.
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
Oh its not just an artifact of logic, it is how the univers works!
Freaky Friday
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
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
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
"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.
When he zoomed in and then flipped over from the Mandelbrot pic to Julia set and then zoomed out again.. Amazing.
You blew up my brain by nerdd :)
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.
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!
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.
Mine is better 😀
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...
My head right now: Stable, unstable, stable stable, unstable
WE NEED THIS TO BE TOP COMMENT PLZ
heheh
😂😂😂😂
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.
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 !!!
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 the single best explanation of the Mandelbrot set I've ever seen. Please do more, or better yet an entire series, using this software!
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.
Wow. That's what I call some exceptionally well spent 16mins 52secs together with my son.
Me: 50+ remembering when my high school suddenly decided to hop on the PC trend that was raging at the time. They splurged on a new computer lab, crammed with 386:s and even the occasional 486 PCs. You had to run to get a seat at one of those super fast ones after school. They would render this new strange computer-math thing they called 'fractals' faster, with more colours. (also Test Drive would run smoother). Mesmerized and frustrated. The impatient feeling of just almost understanding.
Him: 14, like me tired in the morning, like me always late for school. Always liked math, his favourite subject. Oh joy. The sparkle in his eyes watching this! Patient too, stopping the video to explain when I didn't follow. Both laughing, minds blewn and then blewn again.
Thanks!
This is the most incredible explanation I've seen of the Mandlebrot set. I see it, and I understand it!
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?
I think this is one of the best videos of numberphile. The world needs more teachers like Ben. Thanks!
I have a learning disability in mathematics. This had explained a mathematical concept so much better than any teacher I’ve had.
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.
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
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.
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!
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.
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
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!
Crazy how the more you understand it the more you are fascinated by it. Probably the best Mandelbrot Set video on this channel :)
bro i fell in love with the way u teach mathematics, it must be truly inspiring to watch one of ur classes personally
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.
You really should try DMT, experiencing physical reality in 6 spatial dimensions was the most mind-bending experience of my life.
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
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.
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.
This is real mathematican's glory.Because any shape that is on the line just foreverly keeps going and going.It's beautiful
Watching this again. Ben is one of the clearest explainers of complex concepts on Numberphile.
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!
So this finally makes the link between chaos and fractals clear, nice work.
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...
The Julia set thing moving around on the Mandelbrot set was mind blowing
I can barely do simple math but this was explained in such a digestible way, I really understand what mathematicians see in their work.
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 ^^
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.
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
Ben’s passion for teaching is incredible. What a man!
I'm a total layman here. I can now almost understand the Mandelbrot Set. Love it. Great job. Thank you.
Have you heard of the angry cousin of the Mandelbrot set, called 'the burning ship' Fractal
It has French gothic towers, and its spires are more french gothic towers
And those are technically the chaotic regions that aren't part of the set. It's a real brain bender
@@hareecionelson5875 I haven't heard of it. I'll check it out. Thanks.
1:48 I almost feel like crying. Thank you so much! That makes it all so clear!
I'm gonna zoom anyway because it's a whole new adventure everytime!
Ben's videos are genuinely the most interesting and mind-blowing Numberphile content.
"A geography of iterative stability". Wonderful concept
I read about this years ago, kinda understood the basics but it was so vague, than this video actually shows you from the beginning and how they came up with that. I can say i understand it better now, this video rocks
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
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 😂
The enthusiasm is infectious! Thank you for this channel. :)
"You do again and again and find out what happens in the long term"
Dude just explained life in one phrase
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!
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 ^^.
Wow, Ben is a fantastic communicator! Well done!
Congratulations, this video has earned a space on my “best videos possible” playlist. 🥳
never knew I would ever see a guy discuss math so very happilly. like he's bordering onto a secret and can't contain his excitement. Cheers!
One of the most well-done videos. Beautiful and insightful.
I’m not a math nerd but this is fascinating and also makes beautiful art!
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.
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.
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.
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.
Chaos theory: A small change that explodes into uncertainty.
May be 🦋 effect.
@@boteverywherw1376 The butterfly effect is part of the chaos theory.
This video is remarkably one of the most best videos on Mandelbrot Set👍👍
This is the best, clearest and most beautiful explanation of Mandelbrot that I have ever seen. Thank you
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
The diagram is on a brown paper background
More sustainable ;)
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.
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.
What a brilliant brilliant video!!!! 😍
I was also delighted to know that Mandelbrot was alive until recently. Gladly, when I was studying and coding. We used to plot Mandelbrot sets in Python and trip on them. 😄
Wow
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
5:14 It's happening fast, but it seems the instability happens when any 3 points leave the circle. When the 3rd point touches the circle, it becomes unstable.
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!!!!
"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.
He mentions the book Chaos by James Gleick and that is how I found this video because I am reading it now and wanted to understand more about the Mandelbrot set. Thanks
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
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
You mentioned that you know a number is going to explode when the absolute value is greater than 2.
I recently found out that the general formula for the best possible escape radius is 2^(1/(n-1)) where n is the power in the iterative formula. For the Mandelbrot set that's z -> z^2 + c so n=2 which indeed yields 2, but for other powers it's a different number.
2:49 "1 squared is about 1" this high level mathematical analysis is why I've come to love this channel
absolutley insane video, i had a really mad experience on laughing gas where i passed out and saw part of the mandelbrot set zooming in as time slowed massively and i could predict my own thoughts as they were coming to me in real time but my perception was slowed i was aware of fractals and their significance but never watched a video about them or saw a zoom in. was shocked to my core when i finaly watched one a while back and this has done it again
The "B" in Benoit B. Mandelbrot is short for "Benoit B. Mandelbrot"
😂🧠💥
Benoit (Benoit B. Mandelbrot) Mandelbrot
Benoit Benoit (Benoit B. Mandelbrot) Mandelbrot Mandelbrot
.
.
.
Benoit Benoit......... ..... Mandelbrot Mandelbrot
😂
R E C U R S I O N
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. :-)
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.
Great explanation video... even I, a total non-mathematician, could get at least an inkling of how these seemingly magic (and mesmerizing) fractals function.
This is by far one of the better explanations of Mandelbrot on youtube. Thanks for the great videos Numberphile!
I've always known the Mandelbrot Set as "some sort of fractal pattern"... Thank you for making sense of it for me in a visual way that was both stimulating and strangely calming... Thank you. =)
“it’s a geography of iterative stability” nice
This was just beautiful. Thank you for sharing the geogebra files! I am going to use this with my students.
It is amazing how you ask the perfect questions in between the explanation.
This is fantastic. I've always wanted this explained simply to me!
Just went back to the Holly Krieger videos Mentioned... They're really great and follow on well from this . Recommend.