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.

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:


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.

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:

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 ( 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  Then you will have to add the Reaction Grid to the list of Grids.

Building A Portal @ Caerleon Isle until 1/30

Posted in Building with tags , , on January 23, 2009 by Wizzy

Georg Janick asked me to exhibit some of my latest work on one fourth of the sim at Caerleon Isle.  I like being challenged to do these shows because it inspires me to build or create something new.  In this case I spent about a week building a transparent dome around the structure of a 4-dimensional “120 Cell.”  The 120 Cell is equivalent to our own 3-dimensional dodecahedron.  It looks like a geodesic dome, but rather than being made up of triangles, it is made up of pentagons.  Pentagonal struts are structurally strong, but in this case there are two layers (or “shells”) so the structure is especially strong.

Wizard Gynoid's "Portals" Exhibition @ Caerleon Isle

The dome itself was very tedious to build and ended up being about 1000 prims.

Wizzy Gynoid's "Portals"

The exhibit is entitled “Portals” because I seem to be obsessed with the idea of building a portal to higher dimensions, in this case the fourth dimension.  Inside the dome, rotating around the center you will find some pulsating patterns of glowing particles.

Inside the Portal @ "Portals"

Someone commented that the design would make a “kickass” club.  hehe.

Other examples of some of my geometric creations are on hand here at Caerleon.  I am particularly fond of this thing that I call my “Super Duper Star”:

Super Duper Star

This one is quite intricate and precise.  The Golden Ratio is encoded throughout its structure.

A free Open Source version of the basic rezzer script used to build these structures is available, so find it if you can!

Squeezed through the eighth dimensional portal…

Posted in Building with tags , , , , , on November 2, 2008 by Wizzy

Yesterday, my one month occupancy of the Rezzable Visions sim came to an end.  At the end of September, RightAsRain Rimbaud (of Rezzable) challenged me to make my vision a reality.  Thus began October 2008, the most frantic, yet productive month of my Second Life.

My vision was to give the world a glimpse of something truly wonderful and beautiful — the E8 Polytope.

A Polytope is what we would call a polyhedron, only it lives in a higher dimension than our own.  The E8 Group is an elegantly beautiful geometrical lattice.  Some mathematicians call it the most beautiful object known.  The E8 Polytope lives in the 8th Dimension.  Our feeble human minds can’t intuit what an eight Dimensional object looks like, but we can imagine what its three dimensional shadow looks like.  And that’s what this is — one projection, or rotation, of the eight dimensional object and its three dimensional shadow.

I had been building geometric objects in Second Life for over a year.  I started out slow, like we all do.  I took as many building and scripting classes as I could take, but ultimately I found the best way to learn to build in Second Life was to find a good mentor.  Luckily, I found one of the best.  The mentor I found was a builder named Furia Freeloader.  Furia is a master builder and she helped to show me the ropes.

At first, Furia let me build on a private area of her Taris sim.  It was there that I started to hone my skills and zero in on geometric polyhedra.  I built manually and by hand, using only my eye and the SL building interface.  I built a huge, hollow geometric object that I later discovered was called a stellated rhombicuboctahedron.  I made two versions, one of crystal and one that was old and rusty metal.

Then I challenged myself to build the five Platonic Solids.  This proved to be more difficult than it seems.  Second Life’s interface is less than user friendly.  There’s a steep learning curve and the hardest thing was learning its built-in limitations.  The infrastructure has some annoying glitches one has to get used to.

The most annoying of these is the common occurrence of watching the rotation jump to a new setting on its own.  (The rotations are three numbers that define the yaw, pitch and roll of an object you are building.)  One has to achieve a zen-like state of patience when building in SL, and you can’t let these kinds of annoyances become Gumption Traps.  There are many of these one butts heads up against whilst building in SL.

I apologize for peppering my narrative with phrases and notions like Gumption Trap.  I’ll try to explain them as I go along.  Gumption Trap is a term that Robert Pirsig uses in his book Zen and the Art of Motorcycle Maintenance. It’s exactly what it sounds like — a trap that can cause you to lose your gumption.  In other words, you can lose your momentum and the project you are working on can stall out and fail.

We successfully built the E8 Polytope in the early part of September and spent the month tinkering and fine-tuning the presentation.  By “we” I mean Desdemona Enfield and I.  Desdemona and I built the E8 as a team.  At first rezzing, the object appeared at almost 3,000 prims.  Some of the struts flickered a lot, which led to the realization that we had duplicate (or redundant) struts.  The reason for this soon became obvious.

The three dimensional object is a shadow of the eight dimensional object.  When the source object is rotated, some of the struts line up and overlap.  Once we identified these, we were able to remove them and soon the prim count was down to around 1,400.

That last week of September was a frantic one.

Soon the object was demonstrated for physicists from CalTech, the Los Alamos Research Laboratory, the University of Michigan and Saint Lawrence University.  Based on the enthusiastic response, I decided I wanted to show the object at Second Life’s annual Burning Life festival.

I managed to win a Theme Camp plot based on my proposal, but soon discovered the disappointing news that I had only 500 prims to work with on that plot.  It is difficult to squeeze a 1400 prim object onto a 500 prim parcel!

The first plan was to display the 3D object with its 2D shadow cast beneath it on the hard playa ground.  The idea was to imply the existence of a higher dimensional object casting these shadows.  I actually attempted to use a temp rez system to squeeze the object within the required prim count, but this succeeded only in causing the entire Burning Life sim to crash!

After I abandoned that plan, I had to make do with photographs of the object.  I selected other geometric objects that I had found embedded within the 3D structure.  These were beautiful in themselves.  Next, the idea was to provide a link back to the sim where the object was rezzed, so it could actually be seen by those who were interested.

The next challenge arose when the Burning Life Ranger staff objected to the links.  They suggested that this was nothing more than advertising for my home sim, and advertising is banned at Burning Life.  I dug my heels in about that objection and argued that this was for educational purposes and the Rangers backed down and didn’t pursue the issue.

Meanwhile, my friend Glyph Graves was helping me with scripts that allowed the E8 to cycle through the different colored struts of the object.  The struts are colored by strut length.  Displaying only one color at a time revealed interesting sub-structures within the object.

Once that project was completed, RightAsRain Rimbaud came to see the object and it was then that he invited me to fulfill my vision on the Rezzable Visions sim for the whole month of October!

Now I had two big projects to pull off at the same time.  Some days I worked in Second Life for almost 25 hours straight, all the while trying to explore the other builds at Burning Life.

As an artist, I work intuitively.  I trust and let my intuition guide me.  The idea of building the E8 Polytope came to me after watching a YouTube video produced by New Scientist Magazine.  In the video, a physicist named Garrett Lisi proposes a startling new Unified Field Theory using the beautiful geometry of the E8 Group.  After my work of building Sacred Geometry objects in Second Life, the challenge of building the 3D version of the E8 seemed a perfect fit.

I contacted Garrett and proposed my idea.  His enthusiastic suggestions helped to direct the focus of the project to a specific 3D object called the E8 Polytope.  I kept Lisi posted on the progress of the project as it unfolded.

Garrett happens to be a Burner — which means he likes to go to the real Burning Man in the Nevada desert.  I sent him photos of my SL Burning Life plot with the E8 Polytope and its shadow on the playa.  I suggested to him that he should come and take a look for himself.

And then I told him about the Rezzable Visions sim dedicated to the E8 Polytope. The day the sim opened, October 1st, Garrett Lisi’s avatar (named Garrett Netizen) appeared on the sim.  I was in a bit of a state of shock as I showed him around and I noticed that he seemed surprisingly adept for a newbie. (This is not surprising I guess because after all he is a genius.)  Then I tp’d him to the Burning Life camp and it was then that I told him about the official sim opening I had planned for Sunday, October 5th.

I also invited Hamlet Au (formerly Hamlet Linden) to the official opening.

Burning Life ended on Saturday and on Sunday I officially opened the Rezzable Visions sim.  A group of my SL friends were on hand, standing about inside the E8 Polytope when Garrett Lisi appeared on the sim again.  This time Hamlet Au was on hand to document the event.  He published his account of the opening in his New World Notes blog on October 7th.

Meanwhile, Hermes Kondor was so impressed by the sim exhibit that he invited me to do a “conference” on the subject of Sacred Geometry on Sunday, October 12th.  Once I agreed to that I was scrambling to prepare that class and the accompanying slide show. The Sacred Geometry Conference was a big success, with Hermes requesting a continuing class on the subject.

Freelife Magazine’s Lucien Franciosa interviewed me for a feature article and we did a photo shoot.  The article came out in the October 15th issue.

Nepherses Amat next invited me to prepare an art show on the Angelgate sim, to open on October 19th. I decided that the Angelgate show would feature a fourth dimensional object called the 600-Cell Polytope.  While I was preparing that show, Pixels Sideways invited me to participate in another art show at the Caerleon sim.  That show would have a dream theme.

This last news meant that I would again be opening two shows on the same day!  I had a flash of insight and my intuition told me to make an SL replica of Brion Gysin’s Dreamachine for that show.

The Angelgate show opening was a lag-fest as the sim was full to capacity.  I produced a video that introduces the featured object — the four dimensional 600-Cell Polytope — and the many polyhedra I found within it.

The Caerleon art show is a success as well, with some of the best of SL’s builder/artists participating.  It is an honor to be included with the likes of Glyph Graves, Pixel Sideways, White Lebed, Bryn Oh, Olza Koencamp and Blue Tsuki.

And on October 23rd, Cypress Rosewood did me the honor of performing some of his original “Space” music on the Rezzable Visions sim.  Cypress has an audio stream that I find to be appropriate for my builds and I have it streaming at all of them.