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?

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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:

1301

This video lost me at 4:17 I don't understand what the double iteration graph means.

My jaw has dropped when watching this video and I can't find it. It's probably somewhere in the complex plane, in a dark place behind one of the Mandelbrot bulbs. Absolutely mindblowing stuff. 🤯 Thank you!

c+z²=z

Proof of Fermat's Last Theorem for Village Idiots (works for the case of n=2 as well) To show: c^n <> a^n + b^n for all natural numbers, a,b,c,n, n >1 c = a + b c^n = (a + b)^n = [a^n + b^n] + f(a,b,n) Binomial Expansion c^n = [a^n + b^n] iff f(a,b,n) = 0 f(a,b,n) <> 0 c^n <> [a^n + b^n] QED n=2 "rectangular coordinates" c^2 = a^2 + b^2 + 2ab Note that 2ab = 4[(1/2)ab] represents the areas of four right triangles) "radial coordinates" Lete p:= pi, n= 2 multiply by pi pc^2 = pa^2 + pb^2 + p2ab Note that pc^2, pa^2, and pb^2 represent areas of circles, wile p2ab = a(2pb) is the product of a radius (a) and a circumference (2pb). This proof also works for multi-nomial functions. Note: every number is prime relative to its own base: a = a(a/a) = a(1_a) a + a = 2a (Godbach's Conjecture (now Theorem...., proved by me :) (Wiles' proof) used modular functions defined on the upper half of the complex plane. Trying to equate the two models is trying to square the circle. c = a + ib c* - a - ib cc* = a^2 + b^2 <> #^2 But #^2 = [cc*] +[2ab] = [a^2 + b^2] + [2ab] so complex numbers are irrelevant. Note: there are no positive numbers: - c = a-b, b>a iff b-c = a, a + 0 = a, a-a=0, a+a =2a Every number is prime relative to its own base: n = n(n/n), n + n = 2n (Goldbach) 1^2 <> 1 (Russell's Paradox) In particular the group operation of multiplication requires the existence of both elements as a precondition, meaning there is no such multiplication as a group operation) (Clifford Algebras are much ado about nothing) Remember, you read it here first) There is much more to this story, but I don't have the spacetime to write it here. see pdfs at physicsdiscussionforum dot org

U can sort of already see the Mandelbrot set at the first map of Julia’s it’s hard to see

U can find Julia sets IN THE MANDELBROT SET

Why are the sign post branches arbitrarily labelled 1, 2, 3....?

So start z = z^2 + c Second D(f(f (Tried to spam at 197)

I suck at math and can't tell you how much this made my day. You've completely opened my eyes and can't wait to see more. Subscribed.