Wave Articulation Matrix¶

The Wave Articulation Matrix is composed of concentric steel cylinders. The simplest design uses four cylinders. More sophisticated devices
may have 6, 8, or any even number of cylinders.

Fig. 1.1: Wave Articulation Matrix -- 8-Element

All the cylinders have the same mass, and surface area.

The length of the innermost cylinder is equal to the circumference of the outermost cylinder. The length of the outermost cylinder is equal to the circumference of the innermost.

Fig. 1.2: Physical Dimensions -- Side View -- 8-Element WAM
Fig. 1.3: Physical Dimensions -- Top View -- 8-Element WAM
Fig. 1.4: Perspective Views -- 8-Element WAM

The WAM could be described as a Log Periodic Nested Waveguide. It is a Log Periodic structure, in that, the radius or length of each element is equal to that of the previous element, multiplied by some constant. In this case, the constant is the Golden Ratio.

Fig. 1.5: The WAM is a Log Periodic Nested Waveguide

If we want to build a 4-element WAM around a 0.75 inch diameter acetel rod, using 0.002 inch thick steel shim stock, then Lambda = 10.008 inch.

Fig. 1.6: Example Dimensions -- 4-Element WAM
Fig. 1.7: Photo of 4-Element WAM

From a Golden Spiral to Gabriel's Horn¶

I would like to show you how the geometry of the Fountain can be derived from a Golden Spiral.

Let's take a look at a Golden Spiral.

Fig. 2.1: A Golden Spiral

A Golden Spiral is a kind of Logarithmic Spiral. Its radius multiplies by the Golden Ratio every quarter cycle. In the picture, the Golden Ratio is written as the Greek letter Phi.

Just to make things simpler, let's have our Golden Spiral grow by a factor of Phi every complete cycle, instead of every quarter cycle. Let's also look at our spiral sideways, and allow it to exist in the dimension of time. Now what does it look like?

Fig. 2.2: A Golden Spiral in Time

The envelope of the wave on the right is an exponential curve; the amplitude of the wave is growing exponentially.

Can our wave grow in any other way? Yes. Its frequency can grow as well as its amplitude. Let's make a wave where each time it completes one cycle, its amplitude has multiplied by the Golden Ratio, and its period has been divided by the Golden Ratio. Now what does our wave look like?

Fig. 2.3: A Golden Spiral with a Hyperbolic Envelope
Fig. 2.3.1: Explanation of the Logarithm Used in the Equation

This wave has a hyperbolic envelope, not an exponential one, as before.

We can also flip our wave around. This is perhaps the more general form of the equation.

Fig. 2.4: A Golden Spiral with a Hyperbolic Envelope -- a Chirp
Fig. 2.4.1: The Constant K Determines How Quickly the Wave Collapses

If we rotate the envelope of this wave around the Z-axis, we create a Hyperboloid.

Fig. 2.5: Gabriel's Horn

A Hyperboloid is also known as Gabriel's Horn, because it looks like the trumpet blown by Archangel Gabriel on the Last Day. It has finite volume, yet infinite surface area. This is also the correct shape of a vortex in water.

The cylinders of the Fountain are formed by taking slices of Gabriel's Horn.

Fig. 2.6: Wave Articulation Matrix and Gabriel's Horn
Fig. 2.7: Wave Articulation Matrix -- Perspective View

Wiring¶

The circuit used to excite the WAM is very similar to a RADAR Modulator.

Fig. 3.0: RADAR Modulator is very Similar to WAM Exciter
Fig. 3.1: Simple Wiring Diagram

Let's call the innermost cylinder the Primary Axis, and the outermost cylinder, the Control Ring. Regardless of how many cylinders are in the WAM, all the cylinders between the Primary Axis and the Control Ring are tied together electrically, and provide the output of the device.

Fig. 3.2: Output Circuit

We recommend using a Hydrogen Thyratron, Spark Gap, or Gas Discharge Tube as the switching mechanism. This is because these devices switch from "OFF" to "ON" very quickly -- on the order of tens of pico seconds. Some fast IGBTs can switch in 20 - 50 nano seconds, but this is still 1000 times slower than a Thyratron. Why do we need such a fast switch? The switching time is directly proportional to the diameter of the first cylinder surrounding the Primary Axis. The Modes which this cylindrical waveguide can support are around 11 GHz for the 4-element WAM shown above. Larger structures would tolerate slower switching times.

Not a Steady State Device¶

The Fountain is not a steady state device. It is not excited by RF alternating currents. Rather, it is excited by Transients.

Fig. 4.1: Transients vs. Steady State AC

For an excellent introduction on Transients, please see:

Steinmetz, Charles Proteus, Elementary lectures on electric discharges, waves and impulses, and other transients

Transformation Between Gegenraum and Extensive Space¶

It is incorrect to think of the wave phenomena associated with this device as propagating through Euclidean space with a particular phase velocity.

The Fountain is an interface -- a structure that allows for a transformation between two different kinds of space. We do not mean the kind of transformation in Linear Algebra, in which a matrix A transforms an n-dimensional vector into an m-dimensional one. Rather, we indicate a transformation between Euclidean Space (represented by the infinite plane), and Gegenraum, or conjugate space (represented by the Point at Infinite Distance). Consider the concept of "Duality" in Projective Geometry, in particular, that version of Projective Geometry developed by George Adams and Rudolph Steiner.

Fig. 5.1: Growth Measure from Gegenraum to Extensive Space

Recursive Process¶

Editor's note: This technology comes to us by way of people whose native language is not English. We have done our best to express the important concepts involved in clear English. Here, however, we would like to quote verbatim their description of the recursive process which takes place when the Fountain is in operation.

Each time, Fountain Give Life,
Fountain become....

STRONGER.

So the next time, Fountain Give Life,
Fountain Give......

MORE LIFE.

MORE......
Than the time before.

Hai-lah! Fountain Give!