Відео

What took me two days and 100 pages of reading chaotic dynamical systems, you managed to explain it beautifully in just twenty minutes

I always think it's better to simply discuss 2D vectors with the add and multiply rule (adding angles) first. Then we can clearly see why the horizonal axis is equivalent to the real number line. Then we define "i" to be the 90 degree vector. Starting with i = sqrt(-1) is backwards, from the point of view of understanding what is going on!!! For example at 5:30 you say "it is useful to think of i as a 90 degree rotation..." but it would be better to talk about rotations first, then define i as the 90 rotation. Then the whole thing is clear to everybody.

If you consider all values of Z and C as part of a single set, you would get a 4d fractal where any given 2d plane made of the 8 cardinal directions of 4d space is either the mandelbrot set itself, or one of it's infinitely many julia sets

Now this is what gen alpha should be watching every day instead of skibidi toilet

Okay, so this video has single-handedly enabled me to understand this topic to a degree where I can look at different points within the Mandelbrot set and go "Oh, so THAT'S why it looks like this". And also how this set even came to be in the first place. But I have only one question: why? As in: Why DO we even calculate Z = Z² + C? Like, how did anyone even come up with this equation? Why does it exist? I now know the how, I just don't understand the why.

So Benoit Mandelbrot is responsible for my inability to find recipes for almond bread.

Very precise explanation and good visuals. I watched until the end. 👍 However, your voice could do with a little pzazz. 🙄

Seriously underrated, this deserves more than 200k views Edit: I didn't realize you were a Maths Town alt for a few years

Phenominal resolution when zooming into the sets, a trance.

Julia sets can be created using other fractals like the Burning Ship, Perpendicular Burning Ship, Perpendicular Mandelbrot Set, and Tricorn.

This is the Mandelbrot video ever!

e^π +ie^πi +je^πj +ke^πk +le^πl =MC ^2 e^πi-1=0 jkl=0 Quarternion Octonion Principle of the constancy of the speed of light Law of conservation of energy Law of conservation of momentum ζ(s),η(s),Γ(s) The infinite sum of natural numbers is ∞, -1/12 Differential calculus, integral calculus

e^π +ie^πi +je^πj +ke^πk +le^πl =MC ^2 e^πi-1=0 jkl=0 Quarternion Octonion Principle of the constancy of the speed of light Law of conservation of energy Law of conservation of momentum ζ(s),η(s),Γ(s) The infinite sum of natural numbers is ∞, -1/12 Differential calculus, integral calculus

This is more beautiful... e^ix = sum of the series 1 * ix/1 * ix/2 * ix/3.... where ix is radians as a complex number, which calculates cos + i sin simultaneously

Riemann Hypothesis tan(1/2±i) ⇔ tan(π/2) 1⇔π Euclidean geometry sin(0), sin(π/2), cos(0) cos(π/2), tan(π/2)=±∞ Lorenz transformation 1⇔π Non-evident zero point, Self-evident zero points. Unified field theory

Incredible visualisations! I can't begin to think how you programmed that in blender based off the maths, I have been trying to visualise modular forms in Touchdesigner and its extremely challenging. Very impressive stuff 👍

It's so sad that you stopped making these amazing videos 😢

life would be different if I understood what this video means

WOW 😍

this looks like candy

This looks like a fractal.

Hmmmm ... cool picture using math - Close to reality, but NOT actually reality Keep trying ! Tnx

At 10:24 the up and down wave made me think of a heartbeat monitor, I know strange.

M.I.N.D.B.L.O.W.N.

I was wondering what the colours meant

00:06:34 - The Mandelbrot set reveals an infinite number of fractions between 0 and 1, each with its own unique bulb. 00:12:01 - Only rational numbers can find a periodic equilibrium in the Julia set, forming the bulbs in the Mandelbrot set.

-oC3 Mandelbrot

Hi, thank you so much for this video it was really great :)) Just a question though - what do you mean by some values having period of one / period of two (eg at 12:33)? Thanks!

That criticical strip is pretty sharp.

Now, I understand how a Mandelbrot Set is generated. Thank you so much. This is very, very, very useful and well-done video.

I have really appreciated this series. Well done!

So correct me if I am wrong, you state that all points within the set are connected. I do also believe that all points outside the set are also connected. Furthermore, if I am correct, there are absolutely no lines within the set. If you zoom in far enough on any part of the set, you WILL get the minibrot shape. Is that correct?

*ANOTHER SCIENTIFIC PROOF THE TRUTH OF ISLAM* Thank you for your good content. In Islam, this phenomenon is called "AYAATULLAH" or sign of god ALLAH exist who created this universe. There are so many scientific proof of ALLAH exist stated in the Quran Islamic religious document that sent to us through Prophet Muhammad pbuh 1400 years ago. Anyway thank you for creating this scientific fact that is another proof the truth of our religion. Let's go for Islam Kuala Lumpur Malaysia 13 August 2024 ua-cam.com/video/ne0cBBuHJfU/v-deo.htmlsi=HjBGBE3NGi4-LYuA GOLDEN RATIO IS THE SIGN OF GOD ua-cam.com/video/B4OK-Nc7JKo/v-deo.htmlsi=PFsfa5qp-TPzx7Zh

One should know that modular forms graphic is a simplification. The real graphic is in fourth dimension. Si no human being can visualize what it looks like.

This animation is second to none in expressing how supremely smooth functions are where they're analytic. Brilliant work!

wow, thank you so much for that video. it answered some of my very old questions about the mandelbrot set! thank you!!!

How to make such graph animation? Any softwares?

Honestly the relationship between the 2 is SO interesting I never knew this!! And the part where the branches can remember where they were at, that is SO COOL as well

insanly good video. tysm

For the quest, would it help to rotate the thing by 45° clockwise ?

You talked about the boundary of 0.25, -0.75 and -1.25, but what happens in the giant gap from there to the mini mandelbrot at -1.75?

this is hands down the most crystal clear explaination i've seen on the subject. When you master a subject and you are still able to enter a novice's shoes to teach him you reach the master Yoda level of pedagogy. thanks for this video

i want it

These are fantastic!

‭Proverbs 14:13 Laughter might hide your sadness. But when the laughter is gone, the sadness remains. ‭Ecclesiastes 7:3 Sorrow is better than laughter; it may sadden your face, but it sharpens your understanding. When you have sorrows be happy because it sharpens your understanding. ‭Ecclesiastes 7:4 Someone who is always thinking about happiness is a fool. A wise person thinks about death. ‭Proverbs 3:7 Do not be wise in your own eyes; fear the Lord and shun evil. Do not be wise in your own mind be humble and think of others as better than yourself. ‭Proverbs 3:7 Don’t trust in your own wisdom, but fear and respect the Lord and stay away from evil. Read the Bible if you want more wisdom.

This must be my favorite video on fractals. I found a ‘weird’ butterfly effect for the Vesica Pisces surface area coefficient (=4/6Pi - 0.5xsqrt3). Approximately 1.22836969854889… It would be neat to see its behavior as c in the Mandelbrot iteration

Surface(cos(u/2)cos(v/2),cos(u/2)sin(v/2),sin(u)/2),u,0,2pi,v,0,4pi Notice that 4 pi are needed to complete the surface. This is a single sided closed surface. The radially symmetric Klein bottle.

3:10 pause perfect

how did you run that mandelbrot simulation at the end of the video?

Julia wiggly zoom: