2228 pts ยท March 30, 2014
Exploring hyperdonuts, one dimension at a time.
so fucking true, and that review process is rather ugly at times, looking at you Mochizuki and your IUT ....
Toratopes are still an unpublished application of A000669 series-reduced trees and cotangent sphere bundles (combinatorics + topology). The two ways to rotate in n+1 dimensions (bisecting spin/offset revolve) are a 1:1 bijection of the two branching rules of an A000669 tree (add a new leaf to the same branch/add a new branch to a higher level). Within OEIS A000669 , if you have n=5 leaves (5D space) , you get 12 combinations of smooth surfaces: the S^4 and 11 types of 5D donut.
That is correct! There are 3 out of the 10 that simply spin the shape in the 3d graph, with no change to the solution (the donut arrays). Though, there are some other types with higher symmetry, where even fewer rotations make a unique change to the graph.
POVray is still a beast of a rendering engine, even after all this time. plus, modern cpus are sufficient for a personal render farm, now
Oh, we definitely should
Damn, thought it was next year ...
Nope, it's the 3d slice, cutting through it like a knife-blade
First animation made in POVray. Just learning some of the code right now.
it's a way to describe donut like shapes. look up the "n-torus" on wikipedia: https://en.wikipedia.org/wiki/Torus#n-dimensional_torus
calcplot3d , the older java version that only runs on IE11 now
yes, some are rotation, some are translation of the slice
more detail on the math : http://hi.gher.space/forum/viewtopic.php?f=24&t=2414&p=26851#p26851
last ones were shitty. these are clearer and smoother
A cool new 4d shape I discovered a few days ago
mathematically impossible, need at least 3 dicks
yeah, thats 2700 watt-hours of juice! It took me and my friends about 2 months of 5 hr days, spread over a year of time. lots to figure out
Its about 30-35 lbs, paid $4.60 each x 264. Total cost incl 1800w charger, nickel sheet, balance leads, etc, is $2000
an awful lot of saran wrap, too. case design is sealed fairly well, been through several FL afternoon monsoons over 4500 mi so far
This is a slice, varying c, holding a,b,d,t constant
look into my other submissions, you'll find more
yeah, 2D display of 3D shadow object, of a 4D shape
4d shapes are kinda cool, I guess
Yes, the customer had to replace everything
A few more hours. There's some decent gusts in the tree tops. Right now is the final calm, before the real part gets here
ohhhh, yes
https://en.wikipedia.org/wiki/Joseph_F._Cotton#Awards_and_decorations
It starts off with the 3-plane inside a hole (complex solution). Offsetting will bring part of it into the 3-plane, making things appear
Welcome to my daily life
oh, he gone
I'm not a fan of releasing the same content over and over, but some mobile users had trouble viewing the single poster-sized image
so fucking true, and that review process is rather ugly at times, looking at you Mochizuki and your IUT ....
Toratopes are still an unpublished application of A000669 series-reduced trees and cotangent sphere bundles (combinatorics + topology). The two ways to rotate in n+1 dimensions (bisecting spin/offset revolve) are a 1:1 bijection of the two branching rules of an A000669 tree (add a new leaf to the same branch/add a new branch to a higher level). Within OEIS A000669 , if you have n=5 leaves (5D space) , you get 12 combinations of smooth surfaces: the S^4 and 11 types of 5D donut.
That is correct! There are 3 out of the 10 that simply spin the shape in the 3d graph, with no change to the solution (the donut arrays). Though, there are some other types with higher symmetry, where even fewer rotations make a unique change to the graph.
POVray is still a beast of a rendering engine, even after all this time. plus, modern cpus are sufficient for a personal render farm, now
Oh, we definitely should
Damn, thought it was next year ...
Nope, it's the 3d slice, cutting through it like a knife-blade
First animation made in POVray. Just learning some of the code right now.
it's a way to describe donut like shapes. look up the "n-torus" on wikipedia: https://en.wikipedia.org/wiki/Torus#n-dimensional_torus
calcplot3d , the older java version that only runs on IE11 now
yes, some are rotation, some are translation of the slice
more detail on the math : http://hi.gher.space/forum/viewtopic.php?f=24&t=2414&p=26851#p26851
last ones were shitty. these are clearer and smoother
A cool new 4d shape I discovered a few days ago
mathematically impossible, need at least 3 dicks
yeah, thats 2700 watt-hours of juice! It took me and my friends about 2 months of 5 hr days, spread over a year of time. lots to figure out
Its about 30-35 lbs, paid $4.60 each x 264. Total cost incl 1800w charger, nickel sheet, balance leads, etc, is $2000
an awful lot of saran wrap, too. case design is sealed fairly well, been through several FL afternoon monsoons over 4500 mi so far
This is a slice, varying c, holding a,b,d,t constant
look into my other submissions, you'll find more
yeah, 2D display of 3D shadow object, of a 4D shape
4d shapes are kinda cool, I guess
Yes, the customer had to replace everything
A few more hours. There's some decent gusts in the tree tops. Right now is the final calm, before the real part gets here
ohhhh, yes
https://en.wikipedia.org/wiki/Joseph_F._Cotton#Awards_and_decorations
It starts off with the 3-plane inside a hole (complex solution). Offsetting will bring part of it into the 3-plane, making things appear
Welcome to my daily life
oh, he gone
I'm not a fan of releasing the same content over and over, but some mobile users had trouble viewing the single poster-sized image