Table of Contents

- Introduction
- Consciousness Repairing with Synth Sound/Music from Pure Principles
- Learning How to Wave
- Here it is: Actually Plotting the Caduceus Curve
- From 2D to 3D: Plotting the curve in Blender
- Conclusion
- Golden Mean Caduceus Spiral in WebGL 3D (hardware accelerated viewer) and Blender Game Engine
- Applications

**UPDATE 2, July 2011**I have started a new chapter to document using Blender to draw the Grail curve in 3D.

**UPDATE 3, August 2011:** I understood and modified a Blender script for creating curves so that it properly plots the golden mean spiral in 3D.

Extraordinary as it may seem our tribal origins in these Celtic isles in the UK still exists in what is called Sacred Geometry. We see this reflected in the Stone Circles, the Monuments and Celtic Knot Work as well as deep tribal identities that are still practiced to this day.

It has been with some incredulity and self doubt that I have come to realise that what Dan Winter plotted is not poetically described as "The Grail", but, yes indeed, is actually what is referred to in the Grail Quest which codifies the Sacred Geometry that is the basis of sacred understanding of life energies and production of healthy societies. It is no coincidence that the Grail Quest describes a cup containing a life giving elixir. The mathematically plotted Grail that symbolises arrangement of electromagnetic fields does indeed show an infinitely containing structure which is what cells and DNA use to most efficiently arrange containment of life energies. This is indeed the Cup "that never over flows" meaning implosion/containment/fractal embedding of electromagnetic life energies, basically the same thing a Sunflower seed head does to most efficiently arrange it's seeds, but here this is done with electromagnetic fields; life energies. So I've felt a little like Parciful on my Quest. To find The Grail, only to lose it again and then having to survive trials in order to reach its magnificence once again for the final time that brings the truth of The Grail into consciousness. I can see how my witnessing of the almost total loss of life energies and consciousness - the wasteland in the Grail Quest tale that exists before the return of The Grail - which has led me, in my mourning for that which is the warmth of human existence, to that which has had to be discovered again, as it was discovered again before (hence the existence of the this Grail Quest myth in antiquity).

So it was that I stood at the end of the Dragon Line in Cornwall after dreaming the events that happened there. As I looked out over the arch at Lands End I became aware of a formation out at sea. It was called The Knight. Others had stood there, like me, before in previous cycles of This Grail Quest.

What a story for a Spiritual Warrior such as myself. An actual Knight in a modern version of The Grail Quest. How typical of the times that we were living in that I could not see this identity in myself or its connection to our true tribal origins. What could be more natural, more human ? Yet really being and living this kind of Quest was, sadly, sadly seen as evidence of "mental illness". A terrible ruling that reflects the sickness that had taken over in the absence of The Grail.

However as the Grail Quest predicts, when the Grail is won back by me, and many others, I'm certainly not the only Knight. The King will Return. The King represents Christ Consciousness or simply *healthy* consciousness. This is a triad of The King, The Sword and The Land. These three things that are woven together to create life and healthy society. The King; true personal autonomy, or even a real King who does not "rule" but serves his people who are all the rulers of their own destiny. The Sword. That which fights for life and serves justice and peace. The Land. The greater expression of life energies in the ley lines with the stars above, connecting us to the Cosmos. And then of course, The Grail it'self as simply as the pattern in a Sunflower seed head.

OLD INTRO: *So much thanks and Love to my very good friends Dan Winter and the Implosion Group for making my work shareable. We must do away with the Abstract Error and become part of the Universe. Only by sharing fractaly can the work be made truly natural and part of nature. There is no single act of creation ... only an inPHIknit fractal sharing of information. A case in point is on this page. I could keep what I'm doing secret, fearful of how it might be used or that someone would "steal" it off me. But this is wrong approach based on Ego Fear. The work can only truly be completed by inPHIknitly sharing it at many levels - internally and externally. Only then does it become part of the structure of the Universe rather than just another "product".*

Using Phase Conjugation (the creation of something from many smaller little frequencies) and Heterodyning (mixing sine waves that creates a "beat" in volume) along with the Physics of PHI we can create sounds that should heal and repair consciousness. Of course music does this anyway - that's why it sounds good - but the effect can be more specific with the application of "Dan Winter Physics" (actually Ancient Consciousness Physics) that Dan teaches across the world to various folks.

Here is Ableton. Professional DJ and Musician software.

Here the various controls on the VST synth are defined in Ableton so that we can record their movements. Some of them are also linked to the controls on my MIDI keyboard.

This article will progress as I learn how to apply the pure principles using the Synth in Ableton.

Sounds can be engineered using the VST synths. The synth shown in the previous section has a number of preset waveforms as well as the ability to construct new one's. But we can never be sure that the waveforms we are looking for are actually constructed from pure principles - the Mathematics of nature; the Fibonacci sequence and the Golden Mean.

A search turned up a very cool and free (as in libre not source code unfortunately) VST Wavetable synth that can import waveforms based on coordinates stored in a text file.

Now the trick is to calculate the waveform. At the moment I am using Gnuplot to draw the curve. My mathematics is rusty so I am studying an on-line course.

Here it is for those who want to jump straight in .... Lesson 8. Damping and the Natural Response in RLC Circuits. Go down to Case 3 and there it is !

At least, I think it is. That at least appears to be the basic equation that I need to work with to make the waveform. As you'd expect in an Electric Universe the equation is based on circuits; electronics.. ELECTRICITY !

There are other lessons that go through the fundamentals and pure principles from the bottom up.

How to Graph Sine Curves - Including how to find the period of the graph - the span of one sine cycle from left to right.

Lesson 1. Graphs of y = a sin x and y = a cos x

Lesson 2. Graphs of y = a sin bx and y = a cos bx

The lessons are in sequence with back and forward arrows at the bottom of the page.

Lesson 6. Composite Trigonometric Curves has a similar wave form to Case 3 above (at the bottom of the page).

The equations that look to be in the right direction to what I'm trying to import into the VST synth are damping and loss of power as the wave ebbs away in particular capacitor and resistor circuits. This seems to be at odds with the Sacred Science but, if I understand correctly, it is the fundamental Golden Mean heterodyning and conjugation that actually MAKES charge imploding into fractal based inPHInity.

Back to Gnuplot :) More soon.

After much fretting I have actually now imported this curve into Wavedraw.

This was plotted in gnuplot and exported as a table. After editing the table to make it suitable for import into Wavetable it was imported. The use of the two curves above gives a natural sounding church organ like sound. I will put up a recording compared to an actual church organ audio sample and give some other, different, wave based sources for comparison.

A gnuplot user answered my question in the following Usenet (newsgroups) comp.graphics.apps.gnuplot thread.

Plotting cuduceaus curve in gnuplot

It's a bit of a hack (I mean that as a compliment) as it's not a continuous equation that describes the basic sine wave. It is two gnuplot functions that describe the Caduceus wave. However it does appear to be Golden Mean (Phi) plotted and accurate. As far as I can see the ratio of wavelength and amplitude does fractally cascade by phi (I'm sure readers will correct me if the calculation is not accurate).

Actually getting the plot into Wavedraw was a bit hacky as well. The way the curve is drawn leaves gaps in some parts of the curve. Simply joining these ends of the curve over the gaps completes the curve. That meant exporting as a table from gnuplot and editing the resulting numbers - organised as 11 discrete curves.

Gnuplot table export file (text)

The zeroed coordinate entries are the gaps in the curve. Simply removing those and making everything Wavedraw compatible gives this.

caduceus_for_wavedraw_import.txt

caduceus_for_wavedraw_import_inverted.txt

I then removed all filtering and effects that the Wavedraw VST synth is using to be able to hear the pure sound of these two Caduceus waves. Next is to try it in the other VST synth that I have pictured above.

So this has successfully produced a music usable form of this:

Image source: Power Spectral Measurements of EKG and the Earth's ELF Magnetic Resonance.

The next stage is to actually shift the start point of each of the curves to properly match the fractal cascade implosion as measured by HRV and EEG and shown plotted on the http://GoldenMean.info pages. This should work by shifting the scale start point in gnuplot.

I am not completely sure yet of the relationship between the simple Caduceus curve above and the Grail implosion curve, however this is why I started doing this. To understand ! Readers may also guess that from a musical perspective we are simply recreating the wave that any violin player or singer can reproduce at will without the help of any technology or measurements ! But the point here is that, as covered in the EEG document there is a resonant and intelligent nature to these harmonic waves, frequencies or sacred geometries. The document shows that coherent meditation and yoga produces these types of frequency configurations in such a way as to resonate with the Earth field. As is shown on http://GoldenMean.info and http://FractalField.com there are techniques and technologies here that can HARMONISE our world. This is the source of much, if not all, of the pollution and criminality that besmirches our world. It is the result of UNHARMONIOUS living. That is not simply a form of mysticism or New Age philosophy. This has been MEASURED and is a SCIENCE. This means that how we are to proceed to heal these often horrendous problems we have is now clear. The answer is not political but takes the form of practical and passive golden mean technology approaches. As well as ways of thinking and being and of how we relate to ourselves and the people and nature around us.

As part of this restoring inner harmony is crucial so that we can apply these new (many would say ancient) approaches. Music helps anyway, if it's good music, but there are also principles that can make sure health is fully restored.

More investigative notes on the way !

The following paragraphs describe the original file containing the results of an equation that Dan Winter used to plot his Grail Cup. As I found out it is not actually the original formulae for the Grail Cup, only the result of a calculation in Mathematica or MatLab. This resulted in some thrashing around. See below to go straight to the actual formulae that can be used in Blender.

Here are some lines extracted from Grail.m ... the exported vector plotting equations from ~~MATLAB~~ Mathematica.

Line[{{0.007+0.039*Cos[a+-8.800],0.067+-0.004*Cos[a+-8.800],0.039*Sin[a+-8.800]},{0.007+0.044*Cos[a+-8.400],0.076+-0.004*Cos[a+-8.400],0.044*Sin[a+-8.400]}}]

Line[{{0.013+0.038*Cos[a+-8.800],0.066+-0.008*Cos[a+-8.800],0.039*Sin[a+-8.800]},{0.015+0.043*Cos[a+-8.400],0.075+-0.009*Cos[a+-8.400],0.044*Sin[a+-8.400]}}]

Line[{{0.000+1.539*Cos[a+3.200],2.665+0.000*Cos[a+3.200],1.539*Sin[a+3.200]},{0.000+1.739*Cos[a+3.600],3.013+0.000*Cos[a+3.600],1.739*Sin[a+3.600]}}]

The green line is the first line of the plot. Blue, the second line, and purple the last. The Grail.m plot basically plots a single curve and then repeats it by sweeping it around in a circle to create the chalice or grail 3D plot. For Blender we only need a single one of the vectors to render in 3D space as a curve (there are 1985 "Line" vectors in the .m file). This means changing the syntax of one of the vector / matrix math ~~MATLAB~~ Mathematica lines to Python syntax suitable for Blender. This then creates a Vector in Blender that can be turned into a curve. We are basically transferring the basic plot from the engineering math description of it in ~~MATLAB~~ Mathematica to something suitable for rendering in Blender. The Grail.m file is suitable for doing electrical engineering field calculations, but it is not really in a form meant purely for graphic representation. Of course ~~MATLAB~~ Mathematica may actually be able to calculate a sonic representation of the grail plot ... but I don't have a copy and at the moment understanding the conceptual nature of the grail / caduceus plot is more important.

If we look at one of the Blender add-ons - Math Viz - then we see that the syntax is actually very similar to ~~MATLAB~~ Mathematica. However this was simply an initial experiment and a better way is to use Python, see below.

Example of Math Viz line ...

line = [Vector((-2,-1,2)), Vector((-2, -2,0))]

Compare to the first line of GrailCup.m ...

Line[{{0.007+0.039*Cos[a+-8.800],0.067+-0.004*Cos[a+-8.800],0.039*Sin[a+-8.800]},{0.007+0.044*Cos[a+-8.400],0.076+-0.004*Cos[a+-8.400],0.044*Sin[a+-8.400]}}]

The same line deconstructed ...

Line [{{ 0.007+0.039*Cos[a+-8.800]**,** 0.067+-0.004*Cos[a+-8.800]**,** 0.039*Sin[a+-8.800] }, { 0.007+0.044*Cos[a+-8.400]**,** 0.076+-0.004*Cos[a+-8.400]**,** 0.044*Sin[a+-8.400] }}]

There is the basic 3 x 3 list of vectors to make a line. In Blender Python this ends up as ...

import mathutils

a = 1 # amplitude

# note next line WORKS IN CONSOLE

caduceus = mathutils.Vector((0.007 + 0.039 * cos( a + -8.800 ), 0.067 + -0.004 * cos( a + -8.800), 0.039 * sin( a + -8.800)))

Using Math Viz this plots a line ...

line1 = [Vector((0.007 + 0.039 * cos( a + -8.800 ), 0.067 + -0.004 * cos( a + -8.800), 0.039 * sin( a + -8.800))), Vector((0.007 + 0.044 * cos( a + -8.400), 0.076 + -0.004 * cos( a + -8.400), 0.044 * sin( a + -8.400 )))]

But it only draws a straight line ! The syntax is correct but we are not getting a curve yet.

To continue. Bah ! No wonder I've felt like I've been banging my head against a brick wall. This appears to be a Mathematica program file *not* a ~~MATLAB~~ Mathematica file, hence the ~~MATLAB~~ Mathematica documentation for the "Line" statement was not making sense to me, and no wonder ! Here is the doc for Mathematica Line.

Oh ! There's more. This is getting deeply mysterious. I originally obtained this ".m" file on 6th December 2006. To skip a story that probably does not belong here, my memory is very hazy around that period. The ".m" file is intended for display in LiveGraphics3D, a browser plug-in to show Mathematics files.

To continue ... I am now working with RickyBlender on BlenderArtists.org to implement this in Python. See his thread ...

Thread: WIP for spiral and Helix 2D and 3D

The Golden Spiral 2 is the correct spiral. I confirmed this in a phone conversation with Dan Winter. Thanks Dan ! Incidentally I also introduced him to Blender which he said looked fun. Welcome to Blender world Mr Winter ! :)

The Golden Spiral 2 just needs the Z dimension adding to the script. Dan said this is basically in the form ...

x2+y = radius * golden mean = the z value

That's x squared not x * 2.

After some thrashing around above ... success ! Perseverance wins as always.

A single curve that has been duplicated is shown. Compare with the same Golden Mean Spiral at the top of Implosion Group site.

The curve was plotted using a Python script in Blender. Thanks to RickyBlender for his amazing add-on and help with understanding the math. Thanks as well to Dan Winter for encouragement (via a phonecall).

I altered this Spiral add-on script for Blender myself. This was important to understand the principle here at a symbolic/math level. It would not have helped just being handed the answer here and I spent many weeks sweating over the conceptual understanding. This actually reprogrammed my field which had been horribly skewed by the totally abusive and criminal "treatments" in the corporate system of industrialised treatments laughingly called "the health system". There is an important lesson here for abuse survivors or survivors of corrupt treatments of any kind. This is part of the usual corporate technique of inventing and patenting their toxic "solution" which they can then create disease with. The logic here is entirely cynical and may be difficult to face for some people, but once achieved a lot of progress can be made. It is the corporations cash cow. A cash cow for all the people who commit these crimes against humanity, after they are not part of "faceless" corporations. Once an escape is made from their double bind logic marketing speak an escape can be made from the illusion that anything beneficial was going on here *at all*. Then an authentic solution to any health problem can genuinely be sought and applied. Anyway, enough of the ideology, but I've found that it is an important element here.

classGoldenspiral2(bpy.types.Operator):'''Add Golden Spiral 2. Modified by DJ Barney, July 2011.''''''See http://blenderartists.org/forum/showthread.php?225197-WIP-for-spiral-and-Helix-2D-and-3D for full script.'''bl_idname="mesh.primitive_goldenspiral2_add" bl_label="Add Golden Spiral 2" bl_options={'REGISTER', 'UNDO','BLOCKING'} seg1=IntProperty(name="Segments", description="Number segments", default=32, min=4, max=100) nturn=FloatProperty(name="nturn", description="nturn", default=3, min=1, max=100.0) ht=FloatProperty(name="Height/turn", description="Height/turn", default=1.2, min=0.0, max=100.0)defexecute(self, context):globallayers verts1,edges,faces,medges,vid=[],[],[],[],0 seg1=self.properties.seg1 nturn=self.properties.nturn ht=self.properties.ht# R = G^(2 Theta / pi )# R = a1 exp(b1 * phi) b1 =a bs(log(phi)/90)# R= a1* exp(b1 * n)phi=(1.0+5.0**0.5)/2.0# golden ratio ~ 1.618b1=abs(log(phi)/90.0) b2=log(2) a1=1 minag=0 maxag=nturn*360 seg2=seg1*nturn step1=(maxag-minag)/seg2forn1infloat2_range(minag, maxag, 1): ANGTR=n1*pi/180 ro=a1*exp(b1*n1) XC=ro*cos(ANGTR) YC=ro*sin(ANGTR) ZC=ANGTR*ro/(2*pi)# Z axis was added here, this line was taken from the Archimedes Spiral function in the main script and altered by me. "ro" was "ht" which gave an arbitrary 3D spiral. The conceptial leap took place when I understood where the PHI Golden Mean element is defined; "ro" (line 52) is calculated using "b1" (line 39) which itself is based on PHI defined @ line 38. This gives the same proportions on the Z axis as there are on the X and Y axis (X,Y and Z all have the "ro" part); ie. each sweep of the curve is direct Golden Mean proportion to the previous sweep of the curve. This is the mathematically most efficient way in nature to pack things ... leaves, seeds, mollusc homes (the shell) and many other things. In terms of the work here this is the way the human body energy field arranges itself AT ALL LEVELS. Subatomic, DNA, Cellular, Organs, and total body field. Moreso, the same principle should produce the most harmonically rounded and healthy SOUND ... this is in fact what the chakra points are doing at a very high frequency level (outside human hearing). It's also why good music sounds good. the same sacred geometry is at work in the sound frequencies.# "ANGTR" = angle value in radians (line 51). Basically defines the fundamental points of the curve in Blender using "pi/180" - a basic part of circle plotting math. Also related to a conversion from radians to degrees to make the script easier to write and understand.verts1.extend(XC,YC,ZC)# Add vertices# Make edgesifvid>0: edges.append([vid-1,vid]) vid+=1 named1="Golden_Spiral2" mesh=bpy.data.meshes.new(named1) mesh.from_pydata(verts1,edges,[]) mesh.update() obj=bpy.data.objects.new( named1, mesh ) scene=bpy.context.scene scene.objects.link( obj )return{'FINISHED'}####

(note line number are missing in the code above, coming soon)

Please see this page for a hardware accelerated viewer showing the spiral. You will need a WebGL capable browser and system for full WebGL. If you don't then the viewer will still function using just javascript (make sure you have javascript turned on).

Or you can download a visualisation for Windows and Linux that used the Blender Game Engine.

Work is in progress on full WebGL export from Blender. See this video

Winamp has a math engine to calculate oscilloscope effects ("SuperScope") that could benefit from the calculation in the Python above.

It's extraordinary that the Medusa myth appears to contain a massive clue to the solution to this problem. In that myth our hero uses a mirror as a shield to kill the Medusa with it's own reflection. He then cuts off it's head. The Medusa effect is a story about virulent and uncontrolled Kundalini energies as symbolised by the snakes as hair on the Medusas' head (not at all like the balanced energies as shown by the snake heads meeting in the brain in the usual caduceus symbol). This is the state an abuser will be in because they are exhibiting unhealthy forms of sexuality as defined by Reich. The orgasm is not expressed naturally and therefore ends up being expressed in corrupted forms, usually as violence, control or abuses of various kinds. Extraordinarily the myth includes the solution to all this .. THE PHASE CONJUGATE ** MIRROR** principle as defined by Physics. A material that sends light rays back from where they came. The material is similar to the material that solar panels are made of. But in a phase conjugate material the

What distorts consciousness ? The malevolent intent of the abuser. Therefore it is the powerful effect of phase conjugation inherent in consciousness and DNA that can shield the victim *with the MIRROR* of phase conjugation throwing those rays AND ELECTROMAGNETICS right back in the direction they came from - back to the abuser. This removes the distortion in consciousness that the abuser uses to control their victims.

This is shown both in the way consciousness works - self repairing and distortion removing, and is a science known to the ancient world as is shown in the Medusa myth. The "turning to stone" is the huge levels of tension and consciousness blocking that their abuse and out of control Kundalini energies produce in the victim AKA massive Reichian body armouring AKA blocked Kundalini or "angry" Kundalini energies.

Links:

Blender 2.5 Python Vector Arithmetic ... entered directly into python console.

Blender Vector Class (API) ... for 2.49.

Local File attachments:

Attachment | Size |
---|---|

BGA_Caduceus_Golden_Mean_Visualisation_Windows_and_Linux.zip | 35.71 MB |

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