‭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.

ジュリア集合とマンデルブロ、形まで連携しているとは思いもよりませんでした

Great! Here's another fantastic Mandelbrot set: kzbin.info/www/bejne/fIaWq5uZp9uZnsk

The mind of God is beyond us

Are there any tools I can use to help visualise what's going on? In particular, I am interested in playing around with seeing a tiny change in C that causes a chaotic change in the result.

Amazing. Very nicely explained. Thanks!

Great video, thank you!

thx!

13:00

i am inspired by this. thanks for what you do.

Fascinating and beautifully presented, but unfortunately, my mind had no chance of grasping the concept in a mathematical way. Nevertheless, I was intrigued by the depth of complexity in a simple equation.

wonder how many people have had genuine mental breaks because of fractals

thank you for such a clear precise explanation. Im looking forward to watching more of your videos

The poet and Mathematian Without Division.

one of the best video of the internet

k09vjdjreydkudyfy

I don't understand why the Fibonacci sequence emerges from the rational number properties. Additionally, it seems that the _numerator_ of those bulbs follows the sequence as well! How come??

We thank you for the care and thought you put into creating this excellent and succinct exposition of all the main aspects that tease and puzzle so many people who enjoy exploring Mandelbrot Sets and yearn to understand WHY and HOW they behave like this. The visual display of period orbits is particularly illuminating.

what did you use to make these?

can I get a 3d object file for the 13:50 cosz figure so that I can resin 3d print it?

Very interesting - thanks for positing.

0:75

Great^3 +i1!

Just came across this. A second viewing was required before it clicked in my brain. Thanks for an excellent presentation. I feel like I actually understand this well enough to probe further.

i like this julia set remembering that happens on the fractal, it can make some really chaotic zones, like in the bulb near the 0.25+0i point, the patterns get further and further away essentially making little elephants

micro nano universe 👍♥️

This looks beautiful, but the synthetic pads are stabbing my ears

Is the area of the mandelbrot set known (does it approach a limiting value) or is it undefined? I would think it needs to be bounded by the area of the circle with diameter 4.

are there any other sets or are they all based of from the mandlebrot?

What program did you use to visualize this beauty?

ζ

I'm so glad I discovered these.

Name of the music ?

Mandelbrot is the DNA of Julia sets

Bravo! Bravo!