ConwayLife.com

muzik wrote:

gmc_nxtman wrote:One of my favorite songs in a nonstandard time signature is Going Down by Jake Chudnow.

I already knew that one, glad to see someone else here knows it. Vsauce I assume?

Yep.

Also, Undertale has two examples of 5/4, plus a surprisingly accurate pattern for when 4/4, 3/4 / 6/8 and 5/4 are used. Can you guess it?

Most things by Animals as Leaders, Between the Buried and Me, and Haken are in odd time signatures. Those are kind of my fav three bands at the moment. Not sure if anyone else here likes that kind of music - I noticed linking AAL earlier in this thread met with zero response. I'll dump a bunch anyway for anybody interested.

Some parts of BTBAM's Coma Ecliptic album I've listened to enough to dissect their time signature:
25/8: A main theme of Rapid Calm (25v4 drum polyrhythms, woo)
15/8: The Ectopic Stroll's verses
13/8: A gorgeous 30 second bit of Coma Machine beginning 5:30 in.
11/8: Memory Palace, but it's a bit underwhelming since it just feels like 12/8 with a skipped beat.
Also a lot of 7/4 and 7/8.

Other stuff:
11/4: the intro to BTBAM's White Walls.
9/8 without 3/8 subdivision: Haken's Nocturnal Conspiracy's solos, main theme of AAL's CAFO
Another part of CAFO is in some odd#/16 signature I haven't ever solidly figured out.
7/8: Too much to list, most of Haken's stuff, and older BTBAM. Haken gets particularly good at dividing 7/4 and 7/8 into syncopation, further disguising the time signature. This happens on 1985, Initiate, others.
5/8: Ka$cade (AAL) linked above. Also others, including Haken's Pareidolia's main theme. The middle section of Pareidolia goes into (I think) 23/16. It's a little insane. Any other eager counters can check it out at 3:45 in.
5/4: Lots, but I particularly recommend Lapse by Haken.

_zM wrote:Also, Undertale has two examples of 5/4, plus a surprisingly accurate pattern for when 4/4, 3/4 / 6/8 and 5/4 are used. Can you guess it?

The third movement of Alphys is in 5/4, as is the whole of She's Playing Piano which is based off of that. From what I remember, Here We Are is also based off of that and is this in 5/4.

Here is the final version of my desmos solar system. It covers pretty much everything here, (except Phobos and Deimos) so I think I'm good.

Edit: Combined orbits with lists.

It's not creative on my part, and there might not be much interest in it here, but I watch a lot of cartoons. I just recently finished watching Ōban Star-Racers for the first time. I had long been reluctant to watch it due to the strange design choice of not giving the characters noses, but I got used to it pretty fast once I started watching.

I've been working my way through Samurai Jack so that I can watch the new season. I'm partway through season 4 right now, so I'm almost there.

I've also just started watching the recent reboot of Voltron. I'm only seven episodes in, but it's pretty great so far, which I definitely didn't expect of a Voltron reboot.

Over the last two days I created this island (ignore the left, that's a work in progress, and the right, that's someone else's work in progress)

I built a castle in minecraft, I would love to add a screenshot but it's too big for the forums

I got my paphiopedilum glaucophyllum today, and some drosera seeds

gmc_nxtman wrote:I built a castle in minecraft, I would love to add a screenshot but it's too big for the forums

Go to https://postimage.io/ and use [img] tags. Try resizing using paint or something

https://postimg.org/gallery/24qxq4r0/80ca1862/

Does this work?

EDIT: If this doesn't work, I'll try im​gur

That's definitely a 404

Am I the only one who finds it extremely difficult to understand how the excavated dodecahedron is self-dual?

Oh wait here's something in 5/4:

https://www.youtube.com/watch?v=vmDDOFXSgAs

EDIT: Imgur (for minecraft castle):

http://imgur.com/a/pCasO#

Mod edit: files mirrored here:

muzik wrote:Am I the only one who finds it extremely difficult to understand how the excavated dodecahedron is self-dual?

I'm with you there. The polyhedron itself has 12 vertices of maximal radius but it's dual looks to have 60. So the equivalence has to be topological rather than geometric, making it harder to visualize.

It's because the equilateral triangles which appear to be the faces actually meet up in sets of three in the center of the figure to make faces shaped like the vertex figure of a ditrigonal dodecadodecahedron:



This makes 20 faces instead of 60, each one looking like one small equilateral triangle connecting to 3 larger ones. The small equilateral triangle forms the face's convex core, and 20 of them meet up in the center of the shape to form an icosahedron, the convex core of the excavated dodecaedron. So the excavated dodecahedron is not only a stellation of the icosahedron but also a faceting of the dodecahedron, which is required for it to be self-dual.

https://upload.wikimedia.org/wikipedia/ ... n_face.png

I find the name "excavated dodecahedron" slightly misleading, because excavation usually implies an operation where pyramids pointing inward are added to all the faces (which implies that there are 60 faces and 32 vertices), but this is coming from someone who has very strong opinions on polytope names.

Another interesting thing about this polyhedron is that it's topologically regular, with the Schläfli symbol {6, 6}. This leads to a many-to-one correspondence between the faces of the hyperbolic order-6 hexagonal tiling and the excavated dodecahedron.

gmc_nxtman wrote:Oh wait here's something in 5/4:

snares/kicks/hats/crashryde

my 2cents:

7/(2**n): https://www.youtube.com/watch?v=S9TH0owQcJM
11/(2**n) https://www.youtube.com/watch?v=_UhEJqJQ_-8
(5*(2**n)) * (4/4) http://remix.kwed.org/index.php?search=Project+11

You'd honestly think that this would be the dual to the excavated dodecahedron.

Would still probably make a sexy compound with it though.

I was expecting some sort of truncated icosahedron when I clicked that link...

Well, the great dodecahedron is topologically self-dual, like the excavated dodecahedron, because its dual (the small stellated dodecahedron) is also its conjugate (shape made by replacing the coordinates of each vertex by their algebraic conjugates, which in effect replaces pentagons by pentagrams, pentagonal vertex figures by pentagrammic ones, etc.).

Speaking of polytopes, the hecatonicosachoron or 120-cell seems to me like the best contender for a cellular automaton in a spherical manifold. My reasoning is that each dodecahedral cell touches the fewest others as a percentage of the whole figure (only 12 out of 120) and so the zone of influence of a single cell takes a (relatively) long time to encompass the entire universe.
The order-1 Moore neighborhood contains 12 cells plus the center cell,
The order-2 Moore neighborhood adds 32 more cells to this,
The order-3 Moore neighborhood adds 42 more cells,
The order-4 Moore neighborhood adds 32 more cells,
The order-5 Moore neighborhood adds the final cell, antipodal to the original.

This seems like the best contender for a spherical CA based on a facet-transitive uniform polytope (the duoprisms can have unlimited number of cells but half of them are always one level of influence away from any cell) although maybe there are better ones based on non-vertex-transitive polytopes.

I'd like to see a compound fo two excavated dodecahedra as the duals of each other, so I can actually visualise it.

muzik wrote:I'd like to see a compound fo two excavated dodecahedra as the duals of each other, so I can actually visualise it.

It wouldn't be very impressive, as they would either overlap entirely or one would be hidden inside the other as a smaller version of it. This is because each vertex is along the same ray, starting from the center, as the middle of one of the faces. Since taking the dual swaps faces and vertices, it will replace each vertex with a face whose center is directly below or above that vertex. Therefore, the original faces and the dual faces must be along the same rays from the center of the figure. The same argument can be made about the vertices.

I think there is a more interesting way to prove the the dual is a non-rotated version of the original. The excavated dodecahedron has reflexive dodecahedral symmetry. If we look at a spherical tiling where each triangle corresponds to the smallest asymmetric building block of an object with dodecahedral symmetry, we see that each triangle still looks asymmetric. This means that if you were to superimpose two copies of the same object with dodecahedral symmetry, in exactly the same position, there is no way to rotate/reflect one of the two shapes to form a compound, where they are in different positions, that retains the dodecahedral symmetry.

If such a task were possible, it would require the symmetry modules -- but not the asymmetric "building blocks" of each shape -- to overlap. This means that the symmetry modules (the triangles in the spherical tiling) must be symmetric; they would need to carry the same asymmetric block in multiple orientations. But as those triangles are asymmetric, these is no way to preserve the dodecahedral symmetry when taking a compound of two copies of the same shape, except to have them in exactly the same orientation.

All self-dual shapes with non-doublable symmetry (octahedral and dodecahedral symmetry with reflection) have this property. Interestingly, the modules of tetrahedral symmetry are symmetric triangles, and it is indeed possible to have multiple tetrahedra in different orientations share the same symmetry axes, as in the stella octangula.

Randomly generating names for science-fiction planets. I got this one after tweaking the source code for my (borrowed off the internet) generator script:

planetnamer.py wrote:yalitacairiomalizalanondleliacheichevavarizerzanncevajaelozitizenaiacostrigiortasennchalevarim

Really not the best. When I set the range limits to 5<=length<=15 instead of 50<=length<=150, however, it works quite well.

EDIT: Using the program's source code as initialization produces things like this:

planetnamer.py wrote:Namest_fiorgeprgenar_nargv_narkotonulir_finaren(lfistonainalinot(chind_f.chhotengenames

planetnamer.py wrote:Iref-serse[corkomenairgelfrenap(lteliomelecamaond(sam.lefext_foputdilfer_f.chizinurorolsy

Looks like perfectly normal source code to me.

I'm wondering if there is any connection between the R/S configuration of a chiral carbon atom and the right hand rule.

so as we probably all know, the powers of 2 and powers of 5 exhibit some kind of duality with each other, with 1/power of 2 giving a decimal consisting of a power of 5 flanked by many zeroes, and vice versa. Is there a name for this property, and are there any other sequences of numbers that exhibit this behaviour?

4 and 2.5, 3 and 3 1/3, etc. Any two numbers that multiply to give a power of the base you're in.

Was more referring to whole numbers