A place where I try to explain mathematical concepts that interest me in a non-rigorous way. I build handcrafted animations for most of my projects. Most 2D animations are coded in c++. 3D animations are usually build with custom Python scripts for Blender.
This is a Patreon supported channel: www.patreon.com/mathstown
I also operate the "Maths Town" channel, dedicated to fractal art.
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 ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-ne0cBBuHJfU.htmlsi=HjBGBE3NGi4-LYuA GOLDEN RATIO IS THE SIGN OF GOD ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-B4OK-Nc7JKo.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.
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
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
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.
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!
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
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.
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.
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.
