Re: The splendor of true

On 3/10/2025 2:06 AM, efji wrote:

Le 10/03/2025 à 10:04, 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 :
>

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Indeed. Sorry for the stupid question, but the following parts of RH's description:
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Z=aa'+bb'+i(ab'+a'b) and not Z=aa'-bb'+i(ab'+a'b).
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Means a = x component, b = y component, right? ;^o

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Well...
In his disturbed mind, (a,b) = a-b on the x axis :)
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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).
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Humm... I am not all that familiar with the split complex numbers. Something like this?
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glm::vec2
ct_complex_split_mul(
     const glm::vec2& z1,
     const glm::vec2& z2
) {
     return {
         z1.x * z2.x + z1.y * z2.y,
         z1.x * z2.y + z1.y * z2.x
     };
}
>
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Where:
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glm::vec2 s0 = { 0, 1 };
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std::cout << "s0 * s0 = " << ct_complex_split_mul(s0, s0) << "\n";
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outputs:
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s0 * s0 = (1, 0)
>
?

 Yes !
 

Thanks. Actually, this is the first time I used split complex numbers. Well, that's pretty cool. I have to thank Python, you and RH for that. Humm... I wonder what the set would look like using one of my Mulia algorithms or even one of my fractal exploder algorithms on it. Humm...
A Mulia is cleverly combining multiple sets within one iteration. My exploder algorithm tries to "recover" from an escape condition by scaling back the escaping point then trying again several times. It can create some rather interesting formations:
https://www.facebook.com/photo/?fbid=1248023746356621&set=pcb.1248023836356612
Sorry for the FB links... Well, here it is on imgbb:
https://i.ibb.co/tPYDf15j/image.png
A julia explode. Now, it works with any escape time fractal. The Mandelbrot version is interesting as well:
https://www.facebook.com/photo/?fbid=1248548172970845&set=a.110008616824812
https://i.ibb.co/7J6V72f7/image.png
Heck it even works in 3d. For instance, here is one of my Mulias applied to a Mandelbulb:
https://youtu.be/XpbPzrSXOgk
Humm... I wonder what a mulia or exploder looks like with the split complex numbers. Need to get on that!
:^)