The Newton Fractal Explained! | Deep Dive Maths
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- čas přidán 2. 07. 2024
- Discover the fascinating world of Newton Fractals. Join Prof. Jeff Chasnov as he unravels the history, creation, mathematical beauty, and intricate self-similarity of these stunning fractals. Dive into their connections to the complex roots of unity and the Julia set, where abstract concepts meet breathtaking visuals.
00:10 Part 1: Introduction
05:00 Part 2: Newton's Method
09:40 Part 3: Computing the Newton Fractal
11:35 Part 4: The Julia Set
16:20 Part 5: The Fractal Structure
20:52 Part 6: Higher Roots of Unity
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Thank you Jeff for showing the beauty and subtlety of math again! I was in your coursera class before and can't wait to follow your videos.
thank you very Jeff. you brought me back from the math phobia to math fun. i love the way you make it easier to understand.
Awesome and mind-bogglingly well-made! I'm very satisfied intellectually learning about the Newton fractal which I never learned before.
what a wonderful explanation!
Great Explanation
Informative!
Good explanation!
Thank you profesor for this video. You are the best...
Good teacher
Please continue this series..
Wanna see more of this
Great stuff.
Superb video.
This made me miss my numerical analysis course. Great video and presentation.
Thank you Professor for your good explanation
Thx u beautiful explain
Thx for This vídeo!
Very nice
Anybody else here studying the connection between newton's fractals, thought patterns under the influence of psychedelics, and the resulting mandelbrot set being very similar to thoughts structure during a thought loop aka bad trip? If you're here and you're also intrigued about that please let me know, I've been thinking about this for past 3 years and I've found many correlations and patterns, let's think about it together
19:10 my favourite moment, when he uses his cellphone to explain the concept :D
Nice video. But the broccoli made me hungry. Fascinating to see how the whole (graphic) space is filled with points, even with the zero points, without which there is nothing. But wait a minute: without zero there is nothing..? I thought it was the other way around: zero is nothing. I think will just have to watch some more of these movies to grasp that one.
Anyone else getting the creeps learning this? I think "Escape Points" is the creepiest terminology used in math.
Is there any way we could use newtons fractals as a way of creating mathematical concenus within a structure as the derivatives of the function are perfectly Symmetrical with the route. So I guess I mean if there were any outside interference in the structure this could trigger an offset in the systems or symmetry and you would know then that the structure was invalidated. Small grain needing a big brains help please
What does it mean (in terms of gradients or other geometry) to differentiate a function with respect to a complex number z?
Given that z is a 2D variable, what exactly is changing incrementally to cause the value of the function to change?
Both x and y are changing independently. Not all complex functions are differentiable.
@@ProfJeffreyChasnov Thanks - but I'm still not sure. For functions of real variables, if the derivative evaluates to 2 at a point we can say (to a linear approximation) _"as x increases by 1, y increases by 2"_ What is the corresponding statement we could make after evaluating the derivative of a complex function at a point?
So if the derivative evaluates to 3+4i, we would say _"as z changes by ???? f(z) changes by ????"_ ?
In other words, as the domain is a 2D variable, shouldn't the derivative have a directional dependence?
To the commenter "Power Driller" who deleted his comment within 10 minutes of posting .... from the part of your comment I could read on Google notifications, it doesn't seem you understood my question about directional dependence.
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Great explanation nice video -thanks a lot
Oof!!! That's smokin hot!!
Hi I accidentally discovered a formula for finding matrix calculus and I named it the khalam Newton method the method takes the derivative of determinant and it converges very fast I thought it's an discovery if you are intrested we can talk about that
where is explanation?