Phi and Fractals

In the past I was inspired by noticing what seemed to be a similarity between a system that would generate a phi series of frequencies and the system that generates the Mandelbrot Set. I have summarized my research in this document:

Phi Power Series: A description of a series of numbers in the ratio of the golden mean and their associated properties. Also includes a section on frequency modulation and mixing of frequencies of the golden mean.

I have written a java application that allows real-time zoom and pan of the mandelbrot set. Unfortunately wordpress does not host java .class files and I will make this program available as soon as I can find a place for them.


My research info Ferroresonance has also touched on the golden mean. Below are a few snippet’s of comments from the EVGRAY yahoo group that I found interesting.

  • Electrons are transformers; as they need energy to self sustain they acquire energy, as this energy is transferred to spherical standing wave strings they create gravity, M field and E field. Alter any, you alter the nature of the electron “even transform it “. Phi is the only ratio in which waves can “add” and “multiply”, expanding or compressing, non-destructively and infinitely transform of circle to straight line and back again… a spiral in 3d.
  • If the relation is compared to an RF radio antenna, the extra power responds to what RF is called antenna multiplication factor. (“antenna power gain”), where the RV windings are a 3 element circular array or amplitron (in case of prime-mover) and a magnetron (in case of alternator). As in case of an antenna, each element gains are 1.618 over isotropic (this means over dipole used as reference) x Phi 3.141592742 for the 3Phase factor spatial transform field ovoid.
  • universal Phi is 3.141592742 (note for Earth use, Phi and PI are swapped) Universal 4d projection constant is 1.618 (IN resonance energy expands into a logarithmic gain of 1.61803398 responding to a 4d hypercube reflection in 3d matter .) energy diminishes with the square of the distance as area travelled multiplies to the square x phi 3.141592742 (for a 12,000 polygon projection of the sphere to get correct spatial projection.
  • Time decay constant is .382 (standard system entropy) This correlates with Phi and circuit Q (relative also to Kelvin ambient temperature of coil); loss to thermal gradient … IF system is looped electron acquires energy from heat , its spin and ethereal flux …there, (ethereal) is where gravity equation enters as electron goes soft Time where M=MC²/vT , T becomes retrograde creating -G (almost non perceptible if system is entropic. ) .
  • TV: Once resonance is attained the only power needed to maintain it is the one lost in entropy. In MRA as stochastic gain from medium is attained in a self support mode decay is no longer existent where H =I²rT where in a logarithmic gain of 1.618; .382 is extractable as joule potential being non reflective to endotropic source .
  • Non-resonant field travels internally in a wire along with the current (in phase) resonant field travels outside the wire pressed by the internal current pressure inside the wire …(off phase) field forms a magnetic balloon where in standing wave it inflates & deflates imparting the 4d wavicle energyprojection to the aether in contact with the physical resonating element.


I have spent some time studying a new type of math created by Jeff Cook who claims to have found a proof for the Riemann hypothesis. This is one of the most sought after mathematical proofs in history. Wikipedia comments:

“The Riemann hypothesis implies a large body of other important results. Most mathematicians believe the Riemann hypothesis to be true. A $1,000,000 prize has been offered by the Clay Mathematics Institute for the first correct proof.”

If this proof is correct then among other things it should provide a basis for cracking previously unbreakable public key encryption codes. Jeff Cook’s paper is available on his website:

On Neutronic Functions and Undefined Figures in Prime Distribution

My verification of of the first 20 pages is available here:

Chad’s Verification of the Riemann Proof

Has Jeff Cook really found a solution to this problem that has eluded the worlds brightest minds for 150 years? Were it not for my day job and other areas of research I would probably have an answer for this. I hope to complete this work when I have the time.


Steorn’s Magnetometer


A company named Steorn has a magnet motor that they claim defies the physical laws of action/reaction. This motor recently went on display at a public location in Ireland complete with online lectures demonstrating the capabilities of the device.
There are number of informational videos on Youtube including:

How It Works

If you read the description on their website they make it sound complicated…

“The time variant nature of Orbo interactions can be engineered using two basic techniques. The first technique utilizes a method of controlling the response time of magnetic materials to make them time variant. This is achieved by controlling the MH position of materials during permanent magnetic interactions.

The second technique decouples the Counter Electromotive Force (CEMF) from torque for electromagnetic interactions. This decoupling of CEMF allows time variant magnetic interactions in electromagnetic systems.”

Actually the principle is very simple. Take a ferrite toroid and wrap it with 50 -200 turns of magnet wire. If you bring a permanent magnet near the ferrite the field of the magnet will permeate and magnetize the ferrite causing an attractive force. If you send enough current through the coil surrounding the ferrite it will saturate and the attractive force between the magnet and ferrite will be reduced.
Their motor has a rotor with permanent magnets embedded. There are 4 or 8 ferrite cores are placed around the perimeter of the rotor. The North/South orientation of the magnets is not relevant because either pole can cause the ferrites to saturate.
Below is a closeup of the ferrites used in the demonstration.
The key thing to notice here is that Lenz’s law apparently does not apply in this interaction because theoretically the solenoid coil should keep all of its flux inside the toroid and create a shield against interaction with the magnet. The interaction appears to be happening only from the saturation of the ferrite material even with the fields of magnet and coil are 90 degrees to each other. If this were true then Steron would indeed have discovered a new type of electromagnetic interaction.

Real or Not?


Just how real is Orbo? That is one of the concepts I set out answer with some experiments. As a ZPE researcher it is my belief that conversion of the magnetic field into a usable electrical energy is possible and I began my testing of the Orbo system with optimism.

ZPE is not about creating something from nothing: It is about using the zero point of a wave as a means to transform other forms of potential energy like magnetic flux, heat, or particle spin into usable energy in such a way that entropy appears to be reversed. It is a science that is both suppressed and ridiculed and to see a company like Steron make it as far as they have seemed surprising.
I could have built an Orbo motor and made careful electrical and temperature measurements but I decided to take a simpler route and explore the basic physics of the system. My results provide evidence to indicate that:
  • The magnets in the rotor do interact with the field from the coil.
  • The field from the coil expands outside the toroid in certain conditions.
  • Lenz’s law may still apply in this interaction.

Test Setup

Below is the device I used to obtain these results. It is a unique type of transformer with a primary wrapped around a ferrite and a secondary taped to the side.

Transformer specs:

Core: MnZn Ferrite, permeability=5000
Primary: 50 turns 26 AWG magnet wire
Secondary: 8 turns 26 AWG magnet wire
Saturable Transformer
This is the circuit used for driving and measuring transformer characteristics. It is driven with a square wave from a signal generator. This signal goes to a driver that switches a power MOSFET. The Scope 1 probe measures current into the primary and the scope 2 probe measures current in the secondary.
I am including the schematic for the low-side MOSFET driver used. After some trial and error with other experiments I have concluded that this driver works very well and I encourage other people to use it. All the components in the driver can be obtained at Radio Shack.
There is also a permanent magnet (PM) used in the experiments. This magnet is cylindrical and has its poles oriented along the centerline.

Initial Condition

In all of the following scope images the top trace is the primary current and the bottom trace is the secondary. When the primary is driven with 110Khz at 12V the core is brought into saturation. This is indicated by the increasing slope of the current.
The secondary shows almost no current (there is a bit because of slight magnetization and irregular winding). This indicates that the primary drive coil is shielding flux from reaching the secondary.
Case 1

Mode 1: The Magnetometer Effect

When a permanent magnet is brought close to the coil (case 2A) the flux from the PM is coupled with the flux produced by the coil. This flux passes the secondary and generates a current through it.
case 2A
This is indicated by the primary and secondary in the scope trace below. Also notice that the primary no longer goes into saturation and we have a linear slope. This is because the primary coil is working against fields in the toroid in addition to fields in the magnet.
case 2A
In case 2B we reverse the orientation of the magnet and the toroid responds in the opposite direction indicated by the scope trace.
case 2B
case 2B trace
In case 2C the magnet is positioned 90 degrees to the secondary. We can see that the primary does not saturate because the field is coupled to the PM but the secondary has little current. This is because the response is inline with the field of the PM and so no flux passes through the secondary.
Case 2C
Case 2C trace
The secondary responds to the PM with a significant amount of sensitivity. It is such an effective way of detecting a magnetic field that it was invented a decades ago as a toroidal “Fluxgate Magnetometer”.
Fluxgate Magnetometer

When an external magnetic field is applied it causes one side of the toroid to saturate before the other. This creates an imbalance between the left and right side of the coils and causes an EMF to be induced in the secondary.

See these links for more information:

Mode 2: Deep Saturation

If the PM is brought close enough to the toroid then one end of the toroid will go into complete saturation and the response from the toroid will rotate 90 degrees. Regardless of the orientation of the PM the response is the same. This is because one side of the toroid is saturated leaving the coil to magnetize the other side.
Case 3A

Case 3B
We can see that in case 3C moving the PM to the opposite end reverses the flux through the secondary.
Case 3A and 3B trace
Case 3C
Case 3C trace
If we put the PM in line with the secondary as in Case 3D we measure nothing from the secondary. This indicates that no flux (or force) is changing between the magnet and the toroid.
Case 3D

The Centerline Case

Something else to note is that when the magnet is aligned perfectly along the centerline of the toroid there is no force or magnetic interaction between the primary and the PM. This is because the effect that drives the Orbo motor relies on the asymmetry of the external magnetic field. In this case the flux from the PM is distributed evenly throughout all parts of the toroid.
Case 4A


These results demonstrate interactions that are not commonly known in some circles. When the magnet is a sufficient distance from the toroid it operates just like a magnetometer and when the magnet is close enough to saturate one end of the core the other side induces a responding field.
One of the primary arguments implied by Steron’s claims is that the PM from the rotor does not cause a resulting back EMF in the coil. My results show that when coil and PM interact it is because of an asymmetry of flux in the toroid and that this always results in a field being extended outside the toroid that can interact with the PM. This indicates that although it is not immediately apparent Lenz’s Law may be alive and well in this system.