Welcome to numerical-veliz Discussions!

[osveliz]

👋 Welcome!

I am using Discussions as a place to connect with the community. Please use this space to:

• Discuss videos
• Suggest a topic
• Report code issues
• Share thoughts about numerical analysis and computer science

To get started, comment below to share your thoughts with this community. Remember to follow the GitHub Community Guidelines.

[avachon100501]

Hello, Oscar!
The new Discussions feature is very promising.
And here are my thoughts about numerical analysis.

I was introduced to fractals back in the early 2010s (2012, maybe?), and the first fractal that I saw was the Mandelbrot set. Years later, numerical analysis and root-finding algorithms (such as Newton, Halley, Muller, Householder and Steffensen) allowed me to make more amazing fractals. I used very fast and intuitive software such as Kalles Fraktaler, FractInt, Ultra Fractal and ChaosPro to make explorations of such fractals.

With Ultra Fractal, and your videos, I progressed, and even managed to make multidimensional Newton fractals (so far I only did the two-dimensional variant), and I plan on doing Broyden's method, Jenkins-Traub and Lehmer-Schur. These methods may be a little bit more difficult, but it's always a fun challenge. Ultra Fractal also allows you to use different coloring algorithms, such as binary decomposition, exponential smoothing and triangle inequality average.

Here are fractals that I generated with Newton-Bisection and standard Newton's method for the function z^3 - 2z + 2 for comparison.


More here: https://github.com/avachon100501/ultrafractalcollection/blob/main/Root-Finding/Newton-Bisection%20Hybrid.ufm
So, I think numerical analysis is very interesting to explore, and I like that. Keep up the good work!