I’ve been working on very tangible models of both solid spherical crystals of lignin nanotubules, as well as spherical liquid crystals of the same lignin nanotubules, when suspended in a suitable reagent. My latest animation of the coupled rotation of “A Liquid Crystal Sphere” depicts quantum pressure in action, where the motion on the surface of a spherical object is transferred through the whole volume of the object. While I’ve talked about the differences between solids an

In my previous post I presented the general model of cylindrical crystals rotating within a confined lattice. However, without prior knowledge of what I’ve been working on, the model doesn’t really convey too well how this rotation looks like in a crystallite. So, in today’s post I take the model I used in the “Collapsing a Cylinder-Sphere” and “The Trypolite Crystal” posts and make the cylinders rotate. The major practical difference is that the models in my previous posts

I started my blog a bit over four years ago with a post “And Yet it Rotates”. In it I described my first guess at a supramolecular orbital, or a very complex trajectory for the confined closed-loop motion of molecules. While I still definitely believe that molecules mostly move in more-or-less closed-loop orbitals, even when gaseous or liquid, the model that I presented probably isn’t the correct one. Or if it is correct sometimes, it probably doesn’t describe the most common

In my last post, “The Rhombus Twist”, I presented the topological model of forming bent, twisted, seam between two cylindrical segments, where both have been compressed to rounded rhombuses, both where one of the rhombuses has been twisted clockwise and the other one counterclockwise. However, in the post I confessed that while the model was topologically correct, it didn’t quite match the electron microscope image that was the reason why I felt compelled to make such a model

In today’s post I’m finally presenting quite a literal twist to the trypolite crystal. Actually, at first I was planning on just presenting a visualization of the seam in the dodecagonal pyramidal stack, but as I was writing the post, I realized I could do something even better. But before that, let´s recap. In “The Dodecagon Pyramid Stack of Cylinders” post I presented the model for the formation of pyramidal stack of rotating cylinder, that would eventually collapse into de

In my last post “Collapsing a Cylinder-Sphere” I presented a model by which close-packed clusters rotating cylinders collapse into cylindrical crystallites and showed in a simple illustration how these cylindrical crystallites can be compressed into rounded rhombuses. However, for the illustration of a spherical crystallite, I only applied the second-to-last step of collapsed cylinders and left the rhombuses out. The reason for this was that making the rhombus model would be

In today’s post I collapse my lignin cylinders. In my previous post I had presented the uncollapsed model of cylinder stacking into a dodecagon (quasi-hexagon) pyramid. In this model I took an array of close-packed spheres, with a cylinder inside each sphere and showed their alignment once crystallized, but before the actual crystallization. In this model the radius of the cylinder is exactly √0.5, or ca. 0.707 the radius of its rotational sphere. And equally, the length of t

I’ve been working on the problem of crystallizing rotating cylinders into Waterman polyhedra for ages. To some extent I’ve been doing it for over six years, ever since I got the initial idea of the crystal structure of Lignin spheres. However, for some reason I never got round to properly illustrating the shape as a 3D model until two months ago. One of the big problems I had was that I had done a rough illustration of the crystallization model three years ago, which I includ

In my last post I presented the tricolor model of Waterman polyhedra that allowed me to visualize individual planes in this shape much easier than before. Of course, after making the model with spheres, I set about applying it to a Waterman-Lintinen polyhedron made of cylinders, very much like what I had done decently well with two colors. But once I had converted most of the spheres into cylinders, I began looking at the shape with more skeptical eyes than before. The reaso

This past week I’ve been slowly polishing the visual representations of my theory, and in the process I was learning a bit more about how the structure is grown. I had already illustrated the shape in my post “The Perfect Cylinder-Sphere”, but I thought I could make the shape ‘pop out’ more. In the post “The Waterman-Lintinen Cylinder Crystal” I showed the inner structure of the crystal. However, I wasn’t fully happy with the way the coloring expressed the crystal layer. That

Note: I posted a version of this post earlier today, but because I wasn’t happy with how the 3D model looked, I rewrote the text a bit and made a recolored model. In my last post I showed how to cut a cubic array of spheres into quasi-cylindrical zig-zag crystal. At the end of the post, I talked about how the shape can be multiplied into six copies that can be rotated to fill a circular volume with no gaps or overlaps. But it’s one thing to talk about something and another

In my last post I presented The Perfect Cylinder-Sphere, or a way to crystallize cylinders into a sphere. However, in the post I only presented the crust of such a crystal and led the reader imagine how the crystal structure continues to the core of the sphere. However, even when posting the model, I knew most people would be able to imagine the internal crystal structure. The biggest reason for knowing this is that despite knowing the structure of the crust, I couldn’t prope

It’s been nearly two weeks since my last post on The LignoSphere Cylinder Crystal, where I presented the mathematically accurate way to crystallize cylinders into quasi-spheres. Ever since then I’ve attempted to improve the theory, so that I can more closely describe the electron microscopy images that have guided me in working on the theory in the first place. One of the biggest needs for improvement has been how to make the model to produce more spherical crystallites. And

In my last post I presented the Waterman-Lintinen Sphere. The sphere is an adaptation of Waterman polyhedra, but applied to the crystallization of (nano)tubules, or short cylinders, into quasi-spheres with a truncated octahedral core. The only issue I had with the model was that I knew it was a simplified version of the true crystallization of lignin nanotubules, lacking certain elements clearly visible in Electron microscopy of the disrupted crystallization of colloidal lign

Today I’m doing something brash. I’m claiming a geometrical shape as my own. The shape in question both is and isn’t a Waterman polyhedron. Or more specifically the notation of a Waterman ‘sphere’ is non-physical and needs to change to be relevant to the crystallization of nanotubules. To begin, I’ll start explaining how a Waterman polyhedron is defined. According to Wikipedia: A Waterman polyhedron is created by packing spheres according to the cubic close(st) packing (CCP

In my previous post I presented the simple theory of the seeding and growth of truncated octahedral Waterman polyhedra. That is, how to make a sphere of spheres, where the core of the structure is a tiny octahedron of spheres, on top of which a second slightly larger octahedron of spheres is deposited, after which the next layers are truncated octahedra of very specific dimension. Like this: However, this model assumes that the structure grows gradually into a dented cubocta

In today’s post I’m taking a mathematical detour. In most of my posts I’m talking about topic relating to quantum gravity, and lately more specifically quantum pressure. But today, I’ll return back to Waterman polyhedra. I think I’ve mentioned Waterman polyhedra a ton of times in my previous posts, but I can’t remember most of them. I think the most important post and possibly the first one was in the post “Lignin vs Water”, where I describe the crystallization of lignin na

I’ve been slowly writing my quantum pressure manuscript for some days now. In the process I’ve been trying to cut off all the vagueness from my old theory. Besides not really giving a proper mechanism for the curved motion of supramolecular arrays, I didn’t really explain how the precise mathematics that leads to helical toruses also leads to quasi-spherical toruses. But now I’ve started the process of doing exactly that. I’ll first clarify why this is important by giving a

In my last post I presented my revelation that quantum pressure is torque confined in space. In the post I compared the definitions of angular momentum and pressure and realized that the units point to not just a spatial correlation of angular momentum and pressure, but also a temporal one. That is, pressure is angular momentum divided by time and volume. With a bit of handwaving, I simply stated that torque is angular momentum divided by time, and thus pressure is simply tor

In my last post I revealed that my quest to understand quantum gravity led to the discovery of quantum pressure. Not to recap the whole post, the discovery was about applying the ideal gas law, pV = nRT, to my theory of quantum gravity and almost unexpectedly seeing the definition of pressure popping up. I don’t think that my post was very easy to follow. The reason for this was that I had only come up with the realization recently and didn’t really understand the new theor