At long last Wizzy finds the Crystal Matrix, but discovers the Isotropic Grid extends in all directions to Infinity. Slipping effortlessly into meditative trance, Wizzy makes the connection to the Higher Planes…
A Gif version of this also exists:
I’ve been dissecting the insides of the E8 Polytope. I had an intuition that I could find a spiral in it. After analyzing seven sets of squares that descend in size, I created the following:
Then I was able to perceive a single four-color spiral:
Lately, I’ve been rendering some of my RL work in Second Life.
This time, it’s going the other way. I’m painting a painting in Real Life based on some of the work I’ve been doing in Second Life.
I decided to attempt a 3 foot by 3 foot painting of the E8 Polytope. In Second Life, my E8 Polytope is three dimensional (and very complex.) In fact, the latest version has 6,672 prims. (Which makes it hard to find it a home on a 15,000 prim sim.)
Without further ado, here is the front view of the Concentric Circles Rotation of the 4_21 Gossett E8 Polytope:
I’m working on this new thing. It started out as a sketch on graph paper in RL. Then I turned it into a 3 foot by 3 foot painting:
Then I rendered it in prims in SL in 2D.
Then I turned it into 3D in SL.
At the suggestion of Desdemona Enfield, I knocked out some of the cubes and this is the result:
We put those cubes back in and it starts to look like a twisted Mondrian painting:
I asked Xenophile Neurocam if he knew anything about this fractal. Because it’s definitely not the Golden Spiral. It’s not derived from a Golden Rectangle and it doesn’t encode the Golden Ratio or the Fibonacci Series.
My good friend Xeno is so smart. He said look into something called the “Pythagoras Tree.”
Bingo! Discovered by Albert E. Bosman (1891-1961), a dutch mathematics teacher, in 1942.
This version is different from all other variations I’ve seen of the Pythagoras Tree, so I’m calling it an “Electrum Spiral” because it’s definitely not the Golden Spiral. Electrum is an alchemical mixture of Gold and Silver and the other five classical metals.
You can see it at my new parcel on the Caerleon Art Collective sim, courtesy of Georg Janick:
Wizzy keeps building geometric objects of more and more intricacy and complexity. Wizzy’s building is therefore necessarily Extropic.
This is my latest project. A 6672 prim E8 Polytope. This one is more representative of the E8 than any of my previous attempts. It took several attempts to successfully rez this object, and even so the sim creaked and groaned.
This particular rotation of the E8 Polytope is important because it shows *all* 240 of the vertices. Each vertice can be seen above as a meeting of edge struts.
From this angle, we can see a clear hole on this axis going straight down through the object. When flattened down to two dimensions this object would look this:
This 2D version has 240 recognizable vertices or nodes. If Second Life had less perspective programmed into our view, from this axis or view we could see the object like this.
Some of you might wonder why I am so obviously obsessed with this object. It is considered to be the most beautiful and elegant geometric object known to mathematicians. That alone is probably reason enough…
But as I proceed with this obsession, at each step I learn more and more. I gain a more intuitive grasp of what this thing is all about. Each new discovery is a wonder and a joy.
Where do I go from here?
The direction of higher complexity leads from the eighth dimension up to all 248 dimensions of the E8 Group.
The direction of lower complexity leads downward to the G2. The cube-like, hexagonal symmetry of the G2 lends itself to demonstrations of how quarks and the strong force relate.
Next stop, G2.
G2 Proto gave me four regions on the Reaction Open Sim Grid to build and display my E8 Polytopes. So I rezzed the newest E8 “Concentric Circles” on the Wizzy sim and the older E8 “4_21 Gossett” on the Xeno sim next door. I stretched them so that they almost fill a whole sim each.
This is not possible in Second Life due to the stretch limitation of ten meters. The circular base under the E8 in the photo above is 200 meters in diameter.
This is the way the four sims appear on the Open Sim map. Obviously, there’s a problem with the rendering program, but it gives you an idea of the scale.
Reaction Grid (http://reactiongrid.com) seems to have a working relationship with Intel and Microsoft. According to G2 Proto, Intel has developed a strategy to increase the concurrent avatars on an Open Sim to 150. If true, this would be the long-awaited solution to the laggy sim. And he says that Microsoft is bringing their Open Sims to the Reaction Grid. This may mean some good traffic to see the E8 Polytope works that I have done in collaboration with Desdemona Enfield.
Go and check it out and set your draw distance to 512. I recommend downloading the Hippo Open Sim viewer (from http://reactiongrid.com). Then you will have to add the Reaction Grid to the list of Grids.