Re: New way of dealing with complex numbers

On 3/7/2025 3:34 PM, Richard Hachel wrote:

Le 07/03/2025 à 21:50, "Chris M. Thomasson" a écrit :

On 3/7/2025 4:04 AM, Richard Hachel wrote:

Le 07/03/2025 à 12:50, Alan Mackenzie a écrit :

 

Okay. Well. Let's start small. Use your new way to implement the Mandelbrot set and/or any Julia set. Plot the sucker! Then show us the resulting plot...

 Thank you for your answer.
 You raise the problem of Benoit Mandelbrot's fractals. I could not answer that, because I do not know the subject at all.
I just know that it is a mathematical representation that presents a similar structure at all scales. A bit like Russian dolls.
I look on the internet, where it is written that these fractals start from complex numbers of the nature of Z = a + bi.
It is obviously very interesting, but I do not see the difficulty with what I said about complex numbers.
Have you yourself made a fractal using complex numbers? Can you give me the equation? It would be very surprising if with my principles, we did not arrive at anything at all.

I know a lot about fractals of many types... Created a few novel ones. I am interested in seeing how your "new" complex numbers work with them. Here is a fun anime of an older one I did using complex numbers and my experimental formulas:
https://youtu.be/J5Zw_01Ei3I
Read all:
http://www.paulbourke.net/fractals/logspiral
Some music to go with it:
https://youtu.be/1ti2YCFgCoI
;^D
Actually, I make my own music as well. Here is an example, keep in mind that the music is meant for the player to be in time of peril, so to speak:
https://youtu.be/HwIkk9zENcg
Keep in mind that this did not use complex numbers at all. Just one of my experimental n-ary vector fields. Fwiw, my music was made with one of my MIDI plotters. More of my music, again, no complex numbers used here:
https://youtu.be/oVCjAaY1pOY
(a different vibe here...? No running from a scary vector beast or something... Resident Evil style. ;^) lol.)
Start small... Try to implement the Mandelbrot set using traditional complex numbers first. Plot it. Then use your new version, plot it. I am interested in the differences! Also... Well, I was called Chris "Plot Anything" Thomasson by some friends before... ;^D