What advantage of iterative method over direct method for solving a system of linear equation?
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Iteration is mainly used in fractal mathematics.If you talk about fractals,mainly Mandelbrot set or a Julia set,you can not go on without iteration.By iterating you can repeat an equation over and over again so you get the fractal. Complexity of the fractal depends upon iteration.If you want the fractal to be more complex you need to iterate more.
In linear equation you just get a straight line.If you apply iteration you are going to see something amazing.More complex space.One best example is Mandelbrot set.A set of complex numbers.And the iteration formula applied for this set,you can easily find in any numberphile video on YouTube.That would be way better than my explanation.
After iteration,you will find things getting messier.I mean you can zoom in to a fractal as deep as you can and you will see things repeatedly.Becose we iterate numbers.Same things being repeated and it's really awesome I'll give some link below for deep Mandelbrot zoom you need to watch this.
An interesting fact about Mandelbrot set is,you never really reach to anything.As u can see in the image below,you never really know the dark side of the Mandelbrot set you just zoom into the arms.And nobody knows what is in that dark part of Mandelbrot.
If you asking about advantage, I'll say beauty. There are some other fractal like the coach snowflake and dragon curve and sierpinski triangle etc.If you want to dig you have to take look on fractal mathematics.
https://youtu.be/NGMRB4O922I. Iteration formula for Mandelbrot.
Zooming into the Mandelbrot-
https://youtu.be/aSg2Db3jF_4
Bonus: recent studies have on Mandelbrot has come up with something even more sick.The three dimensional Mandelbrot,or should I say mandelbulb.This Mandelbulb is way too complex and beautiful than usual two dimensional Mandelbrot.You can check nobody stopping you.
I've also put a mandelbulb image.And zooming into Mandelbulb can be found here- https://youtu.be/CC-ITpvWIOE. It's all mathematics)
In linear equation you just get a straight line.If you apply iteration you are going to see something amazing.More complex space.One best example is Mandelbrot set.A set of complex numbers.And the iteration formula applied for this set,you can easily find in any numberphile video on YouTube.That would be way better than my explanation.
After iteration,you will find things getting messier.I mean you can zoom in to a fractal as deep as you can and you will see things repeatedly.Becose we iterate numbers.Same things being repeated and it's really awesome I'll give some link below for deep Mandelbrot zoom you need to watch this.
An interesting fact about Mandelbrot set is,you never really reach to anything.As u can see in the image below,you never really know the dark side of the Mandelbrot set you just zoom into the arms.And nobody knows what is in that dark part of Mandelbrot.
If you asking about advantage, I'll say beauty. There are some other fractal like the coach snowflake and dragon curve and sierpinski triangle etc.If you want to dig you have to take look on fractal mathematics.
https://youtu.be/NGMRB4O922I. Iteration formula for Mandelbrot.
Zooming into the Mandelbrot-
https://youtu.be/aSg2Db3jF_4
Bonus: recent studies have on Mandelbrot has come up with something even more sick.The three dimensional Mandelbrot,or should I say mandelbulb.This Mandelbulb is way too complex and beautiful than usual two dimensional Mandelbrot.You can check nobody stopping you.
I've also put a mandelbulb image.And zooming into Mandelbulb can be found here- https://youtu.be/CC-ITpvWIOE. It's all mathematics)
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