Path: ...!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail
From: efji <efji@efi.efji>
Newsgroups: sci.math
Subject: Re: The splendor of true
Date: Mon, 10 Mar 2025 10:46:43 +0100
Organization: A noiseless patient Spider
Lines: 51
Message-ID: <vqmce3$191rj$2@dont-email.me>
References: <iiAmPhnb6ZsFWL9UK83hB6x5ybc@jntp> <vqj5re$iqtc$2@dont-email.me>
 <vqjna0$lmnh$1@dont-email.me> <vqlh9r$114cn$1@dont-email.me>
 <vqm842$18js4$1@dont-email.me> <vqmarn$19276$1@dont-email.me>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Date: Mon, 10 Mar 2025 10:46:44 +0100 (CET)
Injection-Info: dont-email.me; posting-host="c823f54496d225ae0506aec43f46bb31";
	logging-data="1345395"; mail-complaints-to="abuse@eternal-september.org";	posting-account="U2FsdGVkX19LwSjv0AeCMQQnNAiIs1Fm"
User-Agent: Mozilla Thunderbird
Cancel-Lock: sha1:ToUN2+CsGk03UVWN8ASBhXa8nB8=
Content-Language: fr, en-US
In-Reply-To: <vqmarn$19276$1@dont-email.me>
Bytes: 2847

Le 10/03/2025 à 10:19, Chris M. Thomasson a écrit :
> On 3/10/2025 1:33 AM, efji wrote:
>> Le 10/03/2025 à 03:03, Chris M. Thomasson a écrit :
>>
>>>
>>> Indeed. Sorry for the stupid question, but the following parts of 
>>> RH's description:
>>>
>>> Z=aa'+bb'+i(ab'+a'b) and not Z=aa'-bb'+i(ab'+a'b).
>>>
>>> Means a = x component, b = y component, right? ;^o
>>
>> Well...
>> In his disturbed mind, (a,b) = a-b on the x axis :)
>>
>> But forget the pathetic egotic and just try a+jb=(a,b) un R^2 with the 
>> rule (a+ib)*(a'+jb') = aa'+bb'+j(ab'+a'b) which is the rule on the 
>> split-complex set, (thus j^2=1).
>>
> 
> Here is what I got for my little test:
> 
> https://i.ibb.co/WWwhqh9K/image.png
> 
> Oh how fun!

That's what Python found using Wolfram.
That is not surprising :
Mandelbrot set is generated by the iterative sequence:

z_0=(0,0),
z_{n+1} = z_n^2 + c

The set is defined by all the c \in \C such that the sequence (z_n) is 
bounded.

With the multiplication rule used in the split-complex set, it is 
probably easy to show that if |c_1|+|c_2|<1, then the sequence is bounded.

BTW, did you know that the name "Mandelbrot set" is quite an usurpation?
Benoit Mandelbrot did not "find" or be the first to give a definition of 
the Mandelbrot set. It was described by Fatou and Julia before the WW1, 
without any computer graphics, so they probably did not have a real 
vision of it, and Mandelbrot was just the first to make a picture of it 
in the 1980. Adrien Douady, who was a prominent mathematician working on 
the subject in the 80's (Mandelbrot is not a real mathematician), 
decided for this name, instead of Fatou-Julia.


-- 
F.J.