Re: The splendor of true

On 3/9/2025 1:33 AM, efji wrote:

Le 09/03/2025 à 05:35, Chris M. Thomasson a écrit :

On 3/8/2025 3:54 PM, Richard Hachel wrote:

A nice contributor pointed out that the imaginary universe based on i, which is an interesting idea to find roots to equations that do not have any, that is to say, roughly, to find the roots of the symmetric curve pointed at $(0,y) in the Hachel system.
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Although physicists use incorrect complex products, since for me, the real part of a complex product is (aa'+bb'), and not (aa'-bb'), they nevertheless manage to find pretty figures.
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So I wondered, what would happen if, instead of working with their equations, we worked with mine.
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Into what strange world would we fall, if, instead of using Z=aa'- bb'+i(ab'+a'b), we used the much more logical and natural equation Z=aa'+bb'+i(ab'+a'b).
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How would the "Mandelbrot" or the "Julia" obtained be less pretty?
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Isn't beauty the splendor of truth?

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Give me your version of the addition and multiplication functions of your new version, and I should be able to try it out.
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Here are mine, using my JavaScript code from:
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(note: the vectors are 2-ary here)
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https://fractallife247.com/ct_main.js
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For addition:
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function ct_vec2_add(v0, v1) {
     return [v0[0] + v1[0], v0[1] + v1[1]];
}
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For Multiplication:
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function ct_vec2_complex_mul(v0, v1) {
     var x = v0[0] * v1[0] - v0[1] * v1[1];
     var y = v0[0] * v1[1] + v0[1] * v1[0];
     return [x, y];
}
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Also, a length of a vector might be useful to me even though I can infer it from your versions of the two functions above:
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function ct_vec2_length(v0) {
     return Math.sqrt(v0[0] * v0[0] + v0[1] * v0[1]);
}
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function ct_vec2_complex_abs(v0) {
     return ct_vec2_length(v0);
}
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So, give me your versions of the functions using your new stuff, mainly (addition and multiplication), and I will give it a go when I get some free time to burn. Giving me a length would also help me. Otherwise I will just use the traditional version. I am interested in what it might actually look like via a plot...
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 Python already gave the answer. Please read. This silly rule transforms the Mandelbrot set into a square :)
But the dumb man never never read the answers. He is lost in his sick mind.
 

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