Oscar Veliz | Newton Fractals @OscarVeliz | Uploaded 5 years ago | Updated 5 minutes ago
Using Newton's Method to create Fractals by plotting convergence behavior on the complex plane. Functions used in this video include arctan(z), z^3-1, sin(z), z^8-15z^4+16. Example code and images available at github.com/osveliz/numerical-veliz

Correction: The derivative of arctan(x) should be 1/(1+x^2). This error is only impacts the slides, not the numerical examples nor fractals which used the correct derivative. A video covering this mistake can be found here youtu.be/4jw0cjddmB8

Chapters
0:00 Intro
0:16 Convergence Interval Recap
0:42 Imaginary Numbers
1:05 Newton's Method in Complex Plane
1:29 Basin of Convergence
1:38 Arctangent Fractal
1:50 Newton Fractal
2:10 Why Fractals Emerge
2:54 Example z^3-1
4:07 Example sin(z)
4:33 Example z^8+15z^4-16
4:50 Generalized Newton Fractal
5:05 Generalized Newton Fractal Examples
6:16 Summary
6:42 Thank You

Further Viewing:
Newton's Method youtu.be/E24zUEKqgwQ
Newton's Method Interval of Convergence youtu.be/zyXRo8Qjj0A
Newton Bisection Hybrid (Newt-Safe) youtu.be/FD3BPTMGJds
Laguerre's Method and Fractal youtu.be/blOARV4lnIM
Halley's Method and Fractal youtu.be/3WiVGSy_084
Generalized Newton's Method youtu.be/p0SBubUfwiI

Further Reading:
Numerical Recipes http://numerical.recipes/
Wikipedia en.wikipedia.org/wiki/Newton_fractal

#Fractal #NewtonsMethod #NumericalAnalysis