O Campo Primordial é a força primeira e estruturante do espaço, dentro da qual se criam as formas, do átomo à galáxia, dos planetas aos nossos corpos. Este campo engendra o toróide, o ovo eletromagnético primordial da vida, dentro do qual o fluxo e refluxo vital se nutre do núcleo para fora, produzindo a matriz e o padrão, nos quais todas as coisas estão inscritas.
Entre as diferentes formas criadas, existe um campo de ressonância, uma identidade essencial que as liga e vivifica, uma unidade fundamental, que é a sua razão de ser e a sua vitalidade. Este campo primordial é a expressão do Amor cósmico, da Vida Universal, da Consciência Divina, da beleza transcendental, criando espontaneamente o jogo sagrado.
Study unveils a spontaneous toroidal polar topology in the helielectric nematic state
(Zoomed toroidals. Credit: Yang et al.)
"Magnetic and electric dipoles, objects with two oppositely charged ends, have a similar symmetrical structure. One might thus assume that they exhibit similar internal structures and physical states.
Researchers at South China University of Technology in China recently showed that this is not always the case, by examining the topology of an emerging ferroelectric liquid-matter state with polarized helices, known as the "helielectric nematic state." Their findings, published in Nature Physics, show that this state has a spontaneous toroidal polar topology generated through a flexoelectric effect that favors a specific form of splay deformation of polarizations."
(Another zoomed image of toridals. Credit: Yang et al.)
"In some of their previous studies, the researchers showed that a complex polar orientational field is an advantageous feature for the realization of systems exhibiting a nonlinear optical amplification known as phase-matching. As part of their future research, they would like to build on their findings to facilitate the potential development of these systems.
"Polarization engineering in crystal-based ferroelectrics is known to be very difficult," Aya added. "Thus, developing previously impossible polarization engineering in polar fluids and therefore enabling the fabrication of highly efficient nonlinear optical devices will be one of our follow-up targets.""
So just in case you though my game nDimensional Time Travel Chess couldnt get any worse, I fixed the bug that was breaking hypertoroids. This specific hypertoroid is a radial extrusion of a regular torus along 4 dimensional space. We start with an offset circle like so
And we start extruding radially. What that means is we just push out the face a little bit rotating around the center each time. Now in real life these would be infinitely small, we we're working with computers and human time so we just choose small enough steps
Here's what we see a quarter of the way through
Here you can start to see the donut
And here's the finished product.
For step 1 at least. Now we move onto step two. We move the donut back into place of the original circle and repeat the process
Now for the next step things are a little confusing for our 3D human brains no matter what we do, but especially so if we connect the rings like we did last time. So unfortunately we just have to imagine that these are still connected through 4D space, but we'll only show slices where we have enough room to think about them as their own 3D slices
Just like we would be able to imagine traveling along the donut surface between its little rings (red arrow), a 4D creature would be able to easily imagine being able to travel along the donut's themselves (blue arrow) and those two directions are 90 degrees from one another, making them orthogonal and adding an extra-dimension to the surface
Here's how I typically label and refer to these axes
And finally, here's the finished product of step 2
Now if we repeat the process again
Haha just kidding lol. This is already a crazy enough chess board for me personally. Unless... c: But yeah, definitely one of the crazier boards I've made. Haven't played it yet, but if my torus board was any indicator, this one is possibly just, straight up unplayable ngl. Still, might be fun to try anyway
"Auf und ab, rauf und nieder - haste Erkenntnisgewinne immer wieder"
The title approximately translates to "Going above and below, top and down - you'll have gains of knowledge every time".
[2023/11/15] [Black ink and watercolor on paper]
[ID: At the center of the drawing is a black 3-dimensional spiral. It forms a helix trajectory around a horn torus' axis of revolution. It roughly forms a white/grey sphere. Above the spiral is a question mark. Below the spiral is an exclamation mark. The background is watercolored in rainbow colors and merely bright.]