Archive for geometry

Wizzy Seeks Enlightenment

Posted in Dramas with tags , , , on October 14, 2013 by Wizzy

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:

Making the connection to the higher planes.

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The Seed of Life

Posted in Uncategorized with tags , on September 25, 2009 by Wizzy
The Seed of Life Dark

The Seed of Life Dark

The Seed of Life Light

The Seed of Life Light

Double & Single Spirals Into the heart of the E8!

Posted in Building with tags , , , , , on May 6, 2009 by Wizzy

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:

Copyright © 2009 Wizard Gynoid

Copyright © 2009 Wizard Gynoid

Then I was able to perceive a single four-color spiral:

Copyright © 2009 Wizard Gynoid

Copyright © 2009 Wizard Gynoid

E8 Painting in Real Life!

Posted in Building with tags , , , on April 25, 2009 by Wizzy

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:

3 foot by 3 foot painting of the E8 Polytope

3 foot by 3 foot painting of the E8 Polytope

Electrum Spiral @ Caerleon Art Collective

Posted in Building with tags , , , , , on April 11, 2009 by Wizzy

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:

Original Spiral Fractal painting in RL

Original Spiral Fractal painting in RL

Then I rendered it in prims in SL in 2D.

Spiral Fractal rendered in prims in SL

Then I turned it into 3D in SL.

Soror Nishi asks if I could put some steps up to the fractal.

Soror Nishi asks if I could put some steps up to the fractal.

At the suggestion of Desdemona Enfield, I knocked out some of the cubes and this is the result:

spiral-fractal-sans-2nd-cubes

We put those cubes back in and it starts to look like a twisted Mondrian painting:

Copyright © Wizard Gynoid 2009

Copyright © Wizard Gynoid 2009

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.

http://en.wikipedia.org/wiki/Pythagoras_tree

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:

http://slurl.com/secondlife/Caerleon%20Art%20Collective/212/120/27

Evidence of Extropy is in the Building.

Posted in Building with tags , , , , , , , on March 8, 2009 by Wizzy

Wizzy keeps building geometric objects of more and more intricacy and complexity.  Wizzy’s building is therefore necessarily Extropic.

6672 prim E8 Polytope

6672 prim E8 Polytope

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:

The 2D graph commonly recognized as the E8 Polytope

The 2D graph commonly recognized as the E8 Polytope

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.

Another axis of symmetry reveals itself

Another axis of symmetry reveals itself

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.

Not Possible in Second Life – NPISL

Posted in Building with tags , , , , , , on February 6, 2009 by Wizzy

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.

Sim-Sized E8 Polytope

Sim-Sized E8 Polytope

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.

Wizzy's 4 sims @ Reaction Grid

Wizzy's 4 sims @ Reaction Grid

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.

Two Sim-Sized E8 Polytopes - on the left "Concentric Circles - on the right "4_21 Gossett"

Two Sim-Sized E8 Polytopes - on the left "Concentric Circles" - on the right "4_21 Gossett"

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.