More circles on a sphere of cubes 

Unique? surely antipodal ripple centers give rise to equal tilings... It seems to me that it is unique up to all sign changes (±a, ±b, ±c) generically, but I can't prove this. I suspect each ripple center will have its own 'symmetry group' , containing this copy of (C_2)³ but sometimes being larger possibly?

@@alvarol.martinez5230 They’re not completely different, they follow the same patterns but the would also be (to the human eye) rotated or flipped or differently colored.

You just blew my mind too

@@alvarol.martinez5230 not just plusminus, but also reflecting in planes like x=y will give rise to analogous tiling

I have no clue what you're saying

Those cubes are voxels (3D pixels). However, different definitions of voxel may disagree, a voxel could be defined as having ALL faces of the same solid color (a "true" voxel), or it could be allowed to have faces of different colors (just a 3D solid-color cube, no longer a "true" voxel). In this case it's more correct to say these are cubes, not voxels

If you open the shadertoy demo and pause at the first iteration you can see there are shadows on the cubes

@@Rudxain In 3d graphics the word voxel can be as broad as to refer to any volumetric data, it doesn't even need to be cubes. Your definition is a real one, but it's not universal, nor worth correcting over.

@@jasonbourne485 at some of the zoom ins it’s possible to tell there’s a little bit of ambient occlusion

@@ipkcle1500 oh ok, I thought voxels were formally defined

He explained it in a previous video.

I'm a math whiz , what this guy said .

@@ssamreptile7873 Nah, he is no math whiz! He just attended his farm land elementary school! Didn't you learn that?

I'd love to see the apparent spheres on the surface of a hypersphere made out of hypercubes

@Wasnovak I'm no arts graduate but I have read 1984 and know that is not true.

hmm yes the moiré patterns why yes of course

Playing the algorithm to push this answer to the top.

feels to me like it's just a 3D instance of spatial aliasing. in the frequency domain with audio/radio you can see these kinds of aliases from undersampling, repeated over and over but at lower magnitudes. Though in this case I guess the "Nyquist" sample rate to avoid aliasing would be infinity, and the base signal only keeps getting bigger, so the aliases get bigger and bigger.

Great summary!

They are pretty much point objects (unless it’s in the solar system or an entire galaxy or cluster) Pretty sad that they are billions and trillions of km or miles away though would be cool to actually see planets and solar systems outside of our solar system (on a telescope)

You're high, Tweek, go home.

@@clifsportland High on coffee and its caffeine, maybe

What the fuck are you talking about Jesse?

Not wrong at all, i know that as the core of reality, just people making ripples out to other people and people making ripples to other people around them

whoa bro,i dod it too,and fuck me i can see the circles even when he zooms in as long as i unfocus my eyes,sweet find

The sphere is around 500 cubes in diameter - so only half a meter across.

@@henryseg oh. ☹️

Lmao

thanks for the insightul comment. I remember I still had a book on crystallography somewhere

right because it's bitcrushed into cubes instead of smooth lines

Looks like raindrops in a puddle.

not really? Jupiter's storm patterns are still poorly understood-- juno's radar has been able to see around 250 km below the optical surface of the clouds, and even at the depths that it is able to sense, there is still important interactions happening in the fluid. gravitational data suggest that fluid interactions extend even further into the planet, well past the pressure/temperature boundary where ammonia condenses. This is pretty novel stuff and definitely an area of active research. Consider that the (much simpler) boundary interactions between earth's ocean and atmosphere are still an open question in physics: by contrast, this is a very ""simple"" and elegant bit of maths, IMO at least ;)

@@DallinBackstrom I'm 99% sure you're still inside the box. intuition isn't the same for all

@@brucejohnson5786 no one is attacking you malakas. Lack of understanding on your part does not constitute an emergency or require an explanation from my part. I'll rephrase the comment to fit your letterbox "this video makes Jupiter's storm patterns seem really intuitive to me. however your experience with this visualization may vary"

@@ShadowedStickfigure okay boss, I'm not a malakus

@@brucejohnson5786 fooled me

this would be beautiful

You can just open it in shadertoy

It can never be, because what were seeing is not a sphere! A sphere is a continuous collection of all points that exist the same distance away from the origin. Since this created shape is defined as a set of cubes of identical vector length that exist inclusively within a bounding sphere, All of the tangents and tangent planes for any set of three points on this object which fall on the bounding sphere (so the corners of the cube) can expressed as ratios of the dimension vectors, as rational numbers, so they're not continuous. It's missing a tangent of slope pi on the X,Y plane for example, when a sphere would have infinite!. This one has uncountably many holes. If another shape used the same points on that sphere as our cube thing, you could squeeze an infinite amount of surface area into those holes. For the surface area of a sphere to be 6, it would also have to also be every other number greater than 4pi!

@@LaminatedMoth I never said I’d *believe* the 6pi*r^2 number, just that I’d *listen* lol (edit: I also said “convince”, whoops.) the same argument would also tell us that the length of a square’s diagonal is equal to twice its side length, which is also wrong

Check out the shadertoy demo linked in the description.

Well that's what the coordinates mean, the vector is 1 unit long in X direction, 3 units in Y direction, and 2 units in Z direction. Each of those corresponds to a colored side of a cube, so you'll have 1 red, 3 green and 2 blue.

I noticed this as well. The last example (2,4,3) has a base pattern of 2 red, 4 green, 3 blue, and this base pattern is deviated from as one moves away from the intersection of the block-sphere with the tangent plane the vector is normal to.

@@pocarski I think you have the right idea, but aren't you seeing the cubes on a plane perpendicular to that vector?

@@only20frickinletters Yes, this is pretty much why this works. You see more of the color in question when the vector it's perpendicular to points more directly towards you.

Good observation! What you noticed is the correct relationship: the ratio between coordinates is also the ratio of each colour's area. First consider a direction vector of h,k,0 (that is, with h,k,l with z component of zero). This vector lies in the XY plane, and the intersection of the tangent plane to the sphere with the XY plane will be a line. This line in the XY plane is orthogonal (normal) to the normal vector. You can get this orthogonal line by simply rotating the h,k,0 vector 90 degrees. The slope of this orthogonal line - which is also a line along the tangent plane - will just be h/k; that is h units stepping in the y direction of 'rise' per k units in the x direction of 'run'. The y direction step is a unit face orthogonal to the x axis, and the x direction step is a unit face orthogonal to the y axis, so the ratio of h and k (the x and y coordinates of the normal vector) is just the ratio of the 'units' normal to the x axis and the 'units' normal to the y axis - the ratio of red to green, as it were. This relationship between x and y still holds even when the z-component (l of h,k,l) is nonzero. Nonzero z just means each layer of cubes is displaced relative to the next, within each individual layer, the above story still holds. Similarly, by symmetry, the same relationship exists between y and z components, and between x and z components, so the ratio of all three coordinates is the ratio of areas for their respective face colours.

could I find what you refer to on youtube?

It's circles because all plane sections of spheres are circles.

Absent a reason for the sphere to have to expand efficiently, this isn't a complete explanation. Isodoublet's explanation is correct.

@@Salien1999 It’s the only reason required. Everything besides circles wouldn’t make a sphere anymore. isdoublet explained why it looks like circles and I explained why it has to be circles. That’s a difference.

All these squares make a circle.

@@pafu015 Everything besides circles wouldn't make a sphere anymore because all cross sections of a sphere are circles, and all cross sections of a sphere are circles because anything else would make aomething that isn't a sphere. you two have said the same thing, but approaching it from different angles.

Thought the same! I guess generating the graph by discrete values is quite the same we're doing with the minecraft blocks. May have something in common even if it's not exactly the same phenomenon.

By my understanding, when there's a complicated graph, desmos can only show parts of the graph it can resolve accurately using a given sample resolution. The cubic approximation of a sphere can only get so close to the actual sphere because it has a finite number of cubes, which is why the approximation gets closer as the distance between the cubes gets smaller. There may be cubes in the cubic approximation (at a given time in the video) for which the coordinates do actually line up with the sphere perfectly, but everything in between is slightly off. So the link here is that they are both discrete approximations of a continuous shape/graph (That's about as far as i can get with understanding it lol)

Yes

interesting

Helium field ion microscope showing the effect here: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-e7NrwaxR_Ao.html&ab_channel=McGillPhysics

I think you mean zygote lol I’m so cool I corrected someone in a RU-vid comment section

@@Me-xo5tw Oh yeah sry, English isn't my native language