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From: "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com>
Newsgroups: sci.math
Subject: Re: New way of dealing with complex numbers
Date: Fri, 7 Mar 2025 22:14:05 -0800
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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