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From: "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com>
Newsgroups: sci.math
Subject: Re: New equation
Date: Thu, 27 Feb 2025 23:49:54 -0800
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On 2/27/2025 8:51 PM, Ross Finlayson wrote:
> On 02/27/2025 01:46 AM, efji wrote:
>> Le 27/02/2025 à 05:19, Ross Finlayson a écrit :
>>
>>>
>>> Division in complex numbers is opinionated, not unique.
>>
>> :)
>> Hachel has a brother !
>>
>>>
>>> So, the natural products and alll their combinations
>>> don't necessarily arrive at "staying in the system".
>>
>> wow
>>
>>>
>>> Furthermore, in things like Fourier-style analysis,
>>> which often enough employ numerical methods a.k.a.
>>> approximations here the small-angle approximation
>>> in their derivations, _always have a non-zero error_.
>>
>> big time BS :)
>>
>>>
>>> Then, something like the "identity dimension", sees
>>> instead of going _out_ in the numbers, where complex
>>> numbers and their iterative products may neatly model
>>> reflections and rotations, instead go _in_ the numbers,
>>> making for the envelope of the linear fractional equation,
>>> Clairaut's and d'Alembert's equations, and otherwise
>>> with regards to _integral_ analysis vis-a-vis the
>>> _differential_ analysis.
>>
>> Nonsense ala Hachel
>>
>>>
>>> These each have things the other can't implement,
>>> yet somehow they're part of one thing.
>>>
>>> It's called completions since mathematics is replete.
>>
>> A BS-philosophical version of Hachel. Let's park them together.
>>
> 
> Division in complex numbers most surely is
> non-unique, whatever troll you are from
> whatever troll rock you crawled out from under.
> 
> 
> Furthermore, if you don't know usual derivations
> of Fourier-style analysis and for example about
> that the small-angle approximation is a linearisation
> and is an approximation and is after a numerical method,
> you do _not_ know.
> 
> Then about integral analysis and this sort of
> "original analysis" and about the identity line
> being the envelope of these very usual integral
> equations, it certainly is so.
> 
> 
> So, crawl back under your troll rock, troll worm.
> 
> 
> I discovered a new equation one time, it's another
> expression for factorial, sort of like Stirling's,
> upon which some quite usual criteria for convergence die.
> 
> 

How would you implement the following algorithms using your special systems?

http://www.paulbourke.net/fractals/septagon/

http://www.paulbourke.net/fractals/multijulia/

http://www.paulbourke.net/fractals/logspiral/

http://www.paulbourke.net/fractals/triangle/

http://www.paulbourke.net/fractals/fractionalpowers/

http://www.paulbourke.net/fractals/cubicjulia/

ect... ?