99.48.1 Michael Lawrence Morton is now posting ASM data here: 

Page 48

Sections List- 99 Electrons and Mythologies
Impossible Correspondence Index

From: Milamo@aol.com
Date: 12/01/01

Michael Lawrence Morton is now posting ASM data here:


99.48.2 Leedskalnins 7129 / 6105195 (MetPhys) 

From: MetPhys@aol.com
Date: 11/22/01
Subject: 7129 / 6105195

I have been comparing Leedskalnin's numbers 7129 / 6105195 with all combinations and orientations of the 704 (apex) pyramid of numbers and the Sephiroth and have not found any reasonable combination that makes sense.



99.48.3 Galactic Mathematics by Solrion (MetPhys) 

From: MetPhys@aol.com
Date: 11/23/01
Subject: Galactic Mathematics by Solrion

Apollonius.Net - Galactic Mathematics

All critiques are welcome, if you have the time. I'm still skeptical about the recent cataclysmic time-frame and literalism of Velikovski and date these events as much as 160 trillion yrs ago, the documentation of which, is collected but is still being developed into a hypothesis.

Jerry: Within this page is a fractal (5000) of the number 50,000 you were curious about.



99.48.4 Cheops pyramid- 64 cycles of Oeric (99.42.4) (MetPhys) 

From: MetPhys@aol.com
Date: 11/24/01
Subject: 99.42.4 Cheops pyramid- 64 cycles of Oeric


Fourth Dimensional Shift No 22 - Time Spiraling

I am under the impression of an ever tightening exponential spiral (Oeric) until Dec 21, 2012.

On this link, above, it is said the ever tightening time-forward (outer brain mind) spiral imploded exponentially, to 0 in the year 2000.

Knowing the spiral continues, we might conclude, according to the above link, it begins expanding exponentially in the customary 64 multiples again, according to Oeric's multiples, possibly in an opposite, time-reversed (psyche) spiral path.

I also tried to correlate the mentioned link-dates with the Cheops pyramid- 64 cycles of Oeric but found no perfectly matching cycle units of yrs / days / hrs / minutes etc.

My question is this, to all who use the rational and intuitive brains together-

Which is more accurate:

The ever contracting time spiral until 2012, or
The contracting, then expanding spiral to 2012?



99.48.5 Mayan fractals and CODATA Constants (William Johnson) 

From: MetPhys@aol.com
Date: 11/29/01
Subject: Mayan fractals and CODATA Constants (William Johnson)

Unifying Science

Mayan fractals and CODATA Constants


99.48.6 Giza plateau 36:37 :: 56:57? (MetPhys) 

From: MetPhys@aol.com
Date: 11/29/01
Subject: Giza plateau 36:37 :: 56:57?
To: Jerry Iuliano

Untitled Document (Kheraha- Giza plateau)

I'm wondering if the number 56, in the above link, has the same relationship to 57 of your studies, as 36 has to 37, also within your studies.



99.48.7 Holotomic Sequence and Synchrographics (MetPhys) 

From: MetPhys@aol.com
Date: 11/30/01
Subject: Holotomic Sequence and Synchrographics

Syndex: A Synergetic Perspective on Number Dyna

To All,

This study should give us some unique individual insights. Feel free to add your unique correlations, connections, correspondences, twists, turns and interpretations.

I was especially surprised at the Holotomic Sequence beginning with the dodecahedron or, of course, 12 sphere centers surrounding a 13th sphere center, producing the first quasi-spheroid, which I intuitively selected, previously, to construct what we may call the Ultimate Machines which, in its full development, will operate with pure symmetric / asymmetric sound power. This group of 13 is otherwise known as B. Fullers Vector Equilibrium (see attachment).

Unique words: Holotomic Sequence, geodesic, holotomes, synchrographics, quasisphere (geodesic)sphere, palindromic, prime numbers, metrology, numeronomy and fibonacci series offers something for every one to comment upon.



99.48.8 Numbers 5.5, 11, 22, 44, 88, 176, 352 and 5.5 (MetPhys) 

From: MetPhys@aol.com
Date: 12/3/01
Subject: Numbers 5.5, 11, 22, 44, 88, 176, 352 and 5.5

To All,

Within the Universal Harmonics website,

I extrapolated, within the 704 apex pyramid, the missing vertical column numbers associated with the central visible numbers 11 and 44. Beginning at the bottom of the pyramid, the following mean differences are noted between:

5 + 6 / 2 = 5.5
9 + 13 / 2 = 11
20 + 24 / 2 = 22
36 + 52 / 2 = 44
80 + 96 / 2 = 88
144 + 208 / 2 = 176
320 + 384 / 2 = 352
apex 704 = 7 + 4 / 2 = 5.5 = center 0

Within the following file ( http://zero-point.tripod.com/stargoddess/anatomy.html ) I found a similar pattern of 11, 22 and 44 as quoted:

"In the late 1960s, Lisitsyn reported that the Soviets had broken the "genetic code" of the human brain. He stated the code had 44 digits or less, and the brain employed 22 frequency bands across nearly the whole EM spectrum (note the 22 Paths of the Tree of Life, 22 Tarot Trumps, 22 primary archetypal modes of information transfer and feedback)."

"However, only 11 of the frequency bands were independent ("11 is the key to all the rituals."). This work implies that, if 11 or more correct frequency channels can be "phase locked" into the human brain, then it should be possible to drastically influence the thoughts, vision, physical functioning, emotions, and conscious state of the individual, even from a great distance."

(Note: I consider it interesting to understand, not to implement).




99.48.9 The Dropa Stones/Galaxy Clock/UFO's (MetPhys) 

From: MetPhys@aol.com
Date: 12/6/01
Subject: The Dropa Stones/Galaxy Clock/UFO's

Mechanics of NASA UFOs: The Galaxy Clock Home: http://www.ufonasa.com/

To All,

The above link and guests Dan Akroyd and David Sereda (Art Bell guests), have, quite independently it seems, made a connection between the dropa stones found on the Chinese-Tibetan border in 1938 and Sirius which was at 33.33 degrees above the horizon and was directly over the northern African location of the famed Dogon tribe, not directly over the sTs "severed tether" event, with ufo's appearing "behind" the sTs "severed tether" video, which ufo's I had no idea existed until today, 12/05/01. These alleged ufos (multiple) appear as the same shape as the dropa stones, and most interestingly, they take the shape of the customary torus that, has proven to all of us, to be the shape that satisfies the 3rd and 4th power exponent of toroidal spheric systems of universe.

Specifically, what do you make of the above link drawing of the obvious torus with a black hole in the center and the spiraling vortex lines relating to the videos ufo displaying the same characteristics, including the "notch" of the dropa stones and of the ufos?



99.48.10 Correction, 12/15/01: Fwd: Alphanumerics, Nibiru, Synchs (CodeUFO) 

From: CodeUFO@aol.com
Date: 12/7/01
Subject: Alphanumerics, Nibiru, Synchs

My thanks to the eagle-eye of Michael Morton for noticing the following error (of sorts) in my recent post about the Nibiru alphanumerics. Michael is quite correct here. I was getting a little fuzzy in the brain and half asleep by the time I actually got all that down in email form. Now, in my fully awake state (a rare thing, indeed!) I found additional typos in my transposing from paper to email. The most important one involves the five languages mentioned in Hurtak's book "The Keys Of Enoch". In my previous post, the alphanumerics were noted as:


That should have been:

The value of 477 is with the addition of the word "ENGLISH".

My apologies for posting the work prior to double checking the numbers and making sure my transcription from chicken-scratched notes on paper to email was accurate.

In any case the basic ideas remain unchanged. The corrected version is posted here, below Michael's notes. Thanks for the heads-up, Michael. Robert (Metphys) if you posted that paper on the web would you mind replacing it with the following corrected version?

In a message dated 12/14/01 10:31:12 AM, Milamo writes:

<< The 477 ... is actually the_sum_of .. 148 + 153 + 176 .... with 176 the ANV of .. "THE SECRET NUMBER".

So .. in 477 .. you have the_sum_of these 3 phrases;

Were you intending THE SECRET NUMBER as "inclusive" of all 3 of those phrases ? (This would also "include itself", which is kinda neat).

-- Michael L.M. >>




ZERO=64 (1)
*ONE=34 (7).......3-letter set
*TWO=58 (4)......3-letter set
THREE=56 (2)................................5-letter set
**FOUR=60 (6)...............4-letter set
**FIVE=42 (6)................4-letter set
*SIX=52 (7)........3-letter set
SEVEN=65 (2)................................5-letter set
EIGHT=49 (4).................................5-letter set
**NINE=42 (6)................4-letter set


Once again the AlphaNumber Table yields more synchronistic results. Just when I thought I'd about exhausted all the information I could squeeze out of it, I found something I apparently hadn't thought to do before.

I multiplied the actual numbers represented by the alphanumbers in each of the three sets, i.e., 1x2x6, 4x5x9, and 3x7x8, and calculated the sum of the products:

1x2x6 = 12 (A biblically and celestially significant number)
4x5x9 = 180 (Half of 360 and also the ANV of THE GEMATRIA STONE and THE ALPHATABLE IS KEY)
3x7x8 = 168 (Which is also the ANV of THREE+THREE+THREE or LIGHT+LIGHT+LIGHT or 56x3)

12+180+168 = 360, complete circle in conventional degrees.

We recognize 360 as a decimal harmonic of 3600, the supposed orbital period of Nibiru in earth years. I looked at the name Nibiru. I know Sitchin has interpreted the name from the Sumerian to mean "Planet of the crossing". But looking at the word, Nibiru, for some reason now I had an intuition that there was a connection between "Nibiru" and "Number". I found this...


162 and its decimal harmonics is a number we're well familiar with by now.
Remembering that ONE SIX TWO = 144, an important number said to be related to "light" by gematria, I took that cue and decided to work with that one first.

Thinking about the idea of the entire three sets yielding the number 360, symbolizing completeness, I recalled the total sum of the AlphaNumeric Values of the alphanumbers in the Table is 522 (64+34+58+56+60+42+52+65+49+42 = 522). I found the difference between 522 and 360 just happens to be 162=PLANET OF NUMBER. Nice synch.

In the past, I've speculated that the Alphanumber Table had some connection with the Great Pyramid because of various numerical results coming out of the Table. I've shown these results in previous email posts. Now I found myself wondering if there is also some connection to Nibiru. At this point I've lost track of the sequence of calculations which followed. I began scribbling it all down on a piece of paper and just when I thought I'd found everything, something else would pop up. About two hours later I had one convoluted mess on my hands. The paper is so full of numbers and words, there's hardly any white space left. So I'll just try to transfer it all to this email, hopefully in some partially logical sequence. In reality, however, the whole thing is not so linear as it is holographic I guess you might say. In other words, every part just seems to be interconnected with every other part like a web. So I'll just start putting the parts down and hope you can get some idea of the interconnectedness involved.

Nice synch, considering the intuition mentioned above!


(Recall in the Bible... John 1:1..... "In the beginning was the Word, and the Word was with God, and the Word was God." This is a very strange thing for John to have written. What might he have known which would cause him to make such an unusual statement?)

The complete alphabet is composed of 26 letters. Alphanumerics deals with letters and numbers, so I looked at that idea and found:
73 + 26 = 99 = MIND SQUARED = THOUGHT (Planet of the mind, anyone?

I also recognized 99 as the ANV of THIRTEEN. I recognized 13 as half of 26. I know that the number 9 is key to so much of the gematrian/code mystery and that I found the value of 9 hidden within the structure of the alphabet by folding the alphabet in half, yielding 13 pairs of numbers, each pair having a sum of 27; which not only reduces to 9 but is also the ANV of the word CODE.

FOLD THE ALPHABET = 135 (1+3+5=9)

The Sumerians referred to Nibiru as the 12th planet because they counted the sun and the moon plus the other 9 planets. However, we can rightly think of it as the 10th planet.

As has been discussed amongst some of us before, the idea of "reversal" and mirrored numbers seems to play into all of this and, if nothing else, it yields interesting results in many cases, as we can see here:

135 + 531 = 666, one of the greatest mystery numbers.

144 is a key number in the Alphanumber Table as the ANVs of the 3-letter set and the 4-letter set each total 144 (34+58+52=144 and
60+42+42=144). Going back to the 666...
666-144 = 522, the sum of the ANVs in the complete Table.

(Side note: I AM ALPHA AND I AM OMEGA = 144)

A few paragraphs back I noted: THE NINE KEYS = 135
I began to explore this idea, this concept. It was all beginning to seem so self referential:

144 - 135 = 9

I noticed in my book of notes the following:

Looking at the phrase, THE NINE KEYS, I wondered what is the 9th key?

Then I found:

Hmm... What happens if we add 9 to that? I shouldn't have been surprised:


The final number? By golly, it is! LOL! The final number in the series of 0 through 9. Now I'm wondering about the first number and the middle number. The idea of a middle number yielded more results than the idea of a first number. Here's what I found:

THE FIRST NUMBER = 178, not a number that rang any bells. I tried a different one:
THE BEGINNING NUMBER = 187, interesting in that the same digits are just switched around. Still no bells but I did notice the difference between them is 9. Also, the sum of the two numbers is 365, the number of days in a year. Maybe significant, maybe not. It felt a little shallow, like something was missing. But to continue...

THE MIDDLE NUMBER = 153 (a very prominent Biblical/gematrian number. Also the ANV of LETTER+NUMBER)

THE FINAL NUMBER = 148 (also has biblical ties being the ANV of MORNING STAR and JESUS+LUCIFER, and also 148 is the ANV of THE ALPHABET CIRCLE, bringing to mind again the 360 degrees)

These numbers, 153 and 148, yielded some interesting results when combined:

153 + 148 = 301. No bells yet, but watch...
153 - 148 = 5

301 + 5 = 306. Hang on, the bell is coming...
We have to go back and pick up our 360:
306 + 360 = 666 (ding ding ding!)

Moving on...
For some reason this made me think about the 10th planet and the idea that it, too, is a key to our mystery. The 10th key? Hmm...


Remember the two phrases, "THE FINAL NUMBER" and "THE MIDDLE NUMBER" yielded some significant results but "THE FIRST NUMBER" didn't give us a whole lot. That made me wonder, is the "first number" (whatever the hell that might mean!) a secret number? I didn't know, but let's substitute "THE FIRST NUMBER" with "THE SECRET NUMBER" and see what we get:

Okay, now what do we have?
176 + 153 + 148 = 477

477??? What kind of number is that? I'd never come across it before but I did notice it reduces to 9 so, hey, there might be something to it. At this point I'm perusing over what I have so far and I'm drawn to the phrase THE TENTH KEY. Suddenly I'm reminded of J.J. Hurtak's book, The Keys Of Enoch. Hmm...

I get out my copy of the book and take a look at the 10th Key in the book. Right off the bat, I see there might be something here! It talks about languages and numbers! The cover page for the 10th Key says:

"The key languages connecting mind-time warps to interconnecting civilizations and manifestations of higher evolution in our time zone are Egyptian-Hebrew-Sanskrit-Tibetan-Chinese."

Wow, plenty of resonating words there! KEY, LANGUAGES, MIND, INTERCONNECTING, CIVILIZATIONS.

But this next synch sat me back in my chair:

403 doesn't ring any bells, but...

The 10th key of Enoch talks about these five languages and how, when combined, they form a grid "connecting the higher I AM consciousness of Light with the human I AM consciousness of Light through a cosmic light vibration".

There is no mention of the English language. But I wondered, might it not also be somehow involved, maybe in some way for a different purpose? After all, it's sure working some interesting stuff here! Could it be considered a sixth addition to the mix? Let's add the English language and see what we get:


SIXTH KEY LANGUAGE = 189, a key gematrian number. How does it correspond with our newly discovered 477? Pretty well!
189 + 477 = 666

Recall our other two numbers, 148 and 153? Reminder:

Then we found THE SECRET NUMBER = 176 and the sum of those three ANVs was 477.

Recall we combined those first two in an interesting way and arrived at 306 and 360 (see above). Now look what we get when each of those is subtracted out of the 477:

477-306 = 171 = POSITIVE+LIGHT
477-360 = 117 = NEGATIVE+DARK
171+117 = 288 = 144 x 2, or what is known as double light.

This newly discovered "magical number", 477, also combines nicely with 522, the sum of the ANVs of the entire Alphanumber Table:

522 + 477 = 999, the inverse of 666
522 - 477 = 45 = ENOCH, and also the sum of the number series 0 through 9.

2001, Gary Val Tenuta


Date: Friday, December 14, 2001 6:31:12 PM
From: Milamo
Subj: Re: Alphanumerics, Nibiru, Synchs
To: Code UFO

In a message dated 12/14/2001 8:05:39 AM Pacific Standard Time, Code UFO writes:

<< Subj: Alphanumerics, Nibiru, Synchs
Date: 12/14/2001 8:05:39 AM Pacific Standard Time
From: Code UFO
To: Milamo


ZERO=64 (1)
*ONE=34 (7).......3-letter set
*TWO=58 (4)......3-letter set
THREE=56 (2)................................5-letter set
**FOUR=60 (6)...............4-letter set
**FIVE=42 (6)................4-letter set
*SIX=52 (7)........3-letter set
SEVEN=65 (2)................................5-letter set
EIGHT=49 (4).................................5-letter set
**NINE=42 (6)................4-letter set

Once again the AlphaNumber Table yields more synchronistic results. Just when I thought I'd about exhausted all the information I could squeeze out of it, I found something I apparently hadn't thought to do before.

I multiplied the actual numbers represented by the alphanumbers in each of the three sets, i.e., 1x2x6, 4x5x9, and 3x7x8, and calculated the sum of the products:

1x2x6 = 12 (A biblically and celestially significant number)
4x5x9 = 180 (Half of 360 and also the ANV of THE GEMATRIA STONE and THE ALPHATABLE IS KEY)
3x7x8 = 168 (Which is also the ANV of THREE+THREE+THREE or LIGHT+LIGHT+LIGHT or 56x3 ... snip .... >>

Gary ...

This email of yours is one of the greatest things you've ever done. It is one of the biggest "blow-aways" you've ever done. Wow !!!!!

This is a great piece of work, IMO !! And I got a real thrill out of it !!

I did notice one "typo", though .. so I'll just mention it here ... and maybe you actually were giving this number as a "sum" of 3 ANVs .. ?? ...

The 477 ... is actually the_sum_of .. 148 + 153 + 176 .... with 176 the ANV of .. "THE SECRET NUMBER".

So .. in 477 .. you have the_sum_of these 3 phrases;

Were you intending THE SECRET NUMBER as "inclusive" of all 3 of those phrases ? (This would also "include itself", which is kinda neat).

-- Michael L.M.


99.48.11 Feigenbaum and physics (Jerryiuliano) 

From: Jerryiuliano@aol.com
Date: 12/16/01
Subject: Feigenbaum and physics


The number 3.5699.. as it is explained here is when r becomes of infinite cyclic length....." At a bifurcation the system undergoes a massive change in long term behavior. As r is increased, the bifurcations come faster and faster ( look at this as if an accelerating effect) , until finally at about 3.5699.. the cycle length becomes infinite.... if r is further increased from 3.5699.. up (but still below 4.0) then the system no longer has a cycle, it bounces about forever, but never repeats itself...."

As I see it, this means the neutron Mev/(c^2) (where c is the amplitude and accelerating module from its squareness) is nothing but the "condensation" line of the chaotic zero-point energy of the virtual reality structure ...in a quantum sense.All reality does not exist beyond this point of the bifurcation tree,3.5699.. limit. This reality is structured by the condensation of the virtual infinite chaos of the zero-point energy void ruled by the Feigenbaum constant (4.669201609..). The Feigenbaum constant is determined by the reciprocal of the growth / decay limit where there is an infinite cycle before chaos. If the Feigenbaum constant determines the ratio of self-iterated cycles, then the Feigenbaum point determines this actual limit (neutron energy) point before and after chaos:

1+[1/((IN3.569904532)-1)] = Feigenbaum constant = 4.669201609

Since 3.569904532 is the actual limit allowed in cyclic structure then it's DECAY function represented by the reciprocal natural log e (IN) shows the real source of the Feigenbaum generated neutron, (similar to compound interest formulas)

((3.569904532^3.569904532)*10) - [1/[(log(sqrt1/FSC))*(10^2)]] = 939.565328976

NIST 1998 for neutron =939.56533

Where FSC = fine-structure constant = 1/137.03599976

The uncorrected form using the "condensation" limit 3.5699....:

(3.56990015^3.56990015)*10 = 938.5653321

To approximate the proton energy (NIST 1998 = 938.271998), divide the correction factor by one-thousandths Pi +1 and subtract from the neutron energy:

1.00318099+[31*1/[(log(sqrt1/FSC))*(10^2)] + proton = neutron

Since there are 31 FSC's from the neutron to the proton counting the extra 1 to go to beyond the Feigenbaum virtual chaos boundary (3.5699..) means a total of 32 changes of amplitude from Feigenbaum to the proton , with neutron at step one and the proton at step 32. To express the proton in a purely mythological context use the Hebrew Talmudic mythological number of the "288 sparks from broken vessels" to represent the stuff of the virtual energy chaos ether and let 288 sparks"represent the exact base for Natures representation of matter:

PROTON: = 938.271998 = pmev

pemv = [288^(2*(emev^(ht/2/bl)))]/10 = 938.271998

where ht = height Cheops pyramid (486.256) = 486.255745

where bl = base leg Cheops pyramid (763.81) = 763.81

where emev = electron Mev/(c^2) = .510998902 (NIST 1998)

How does one extract the value of the electron out of the entangled proton formula? The extraction is done by use of the Feigenbaum point 3.5699.. with the electronic coupling bridge that exists between the proton and the neutron, fermi-coupling charge or the weak force: G(w)= .0000116639(2) (NIST 1998)

Using the uncorrected formula for the neutron and determining the Feigenbaum constant for that single point one gets:

(3.56990015^3.569990015)*10 = 939.5653321 = neutron

such that the Feigenbaum RATIO is derived as:

1+[1/((IN3.56990015)-1)] = 4.669218133 = Feigenbaum derivative

Substituting into the electron formula:

emev = [288^(2*(emev^(ht/2/bl)))]*.00001166399955*4.669218133

or in other words the seed of the neutron 3.5699.. that exists as the last infinite cycle before chaos creates the self -iterated electron. The existence of matter that rides on the cusp of Natures bifurcation tree that is ruled by Feigenbaum constants, implies that the electron is continually being created out the rolling action at the cusp of this edge between chaos and stability. To create the proton one merely eliminates any connection to the Fermi-coupling charge and its association with the virtual reality that exudes out of the chaotic field ruled by Feigenbaum constants:

pemv = [288^(2*(emev^(ht/2/bl)))]/10 = 938.271996

where ht =486.255745


Comparison of the two forms:

pmev = [288^(2*(emev^(ht/2/bl)))]/10 = 938.271996

emev = [288^(2*(emev^(ht/2/bl)))] * G(w) * F = .510998902 = emev

where F = [1/[(IN((939.5653321/10)^(1/3.56990015))-1]]+1 = 4.669218133

All equations reduce to this form:

.510998902/.00001166398756/4.669218136/10 = proton =938.271996

or the electron divided by the fermi-coupling charge divided by the neutron bifurcation point(Feigenbaum) equals the energy of the proton:

emev/G(w)/F(nmev) = pmev

J.Iuliano <<

The Logistic Equation

A particularly interesting, and popular iterated map is the logistic map. This map shows many of the features that we will see appearing later on in continuous systems. The logistic equation is actually a simple model for species population with no predators, but limited food supply. It is given by the following equation:

where r is a parameter to be set anywhere from 0 to 4. The initial x must be from the region 0 to 1. This equation is much more difficult to analyze on a calculator, so we will be using a java applet to help with the analysis. To start, we will be setting r to 2.9. To see what happens, we plot a time series plot of the orbit. As the function is iterated it approaches a stable point. This is similar to the exercise performed earlier. There is actually an unstable fixed point at 0, try plugging zero into the equation for x and see what you get. This point is unstable because if the initial conditions do not start exactly on zero, then they will go to the stable point. The origin is called a repeller, while the stable point is an attractor. In the population example, the origin corresponds to a zero population. Life does not spring from nothing. The parameter r is the amount of food supply. For this amount of food supply the population grows to a point, then settles down to a steady state.

If we increase r past 3.0 then something more interesting happens. The orbit does not settle down to a fixed point. The fixed points that were there before have lost stability, now the system will cycle between two points. This is called a stable cycle, in this case, a stable 2-cycle. In our population, the food has been increased. Now a small generation has so much food that it makes a rapid growth spurt, however, in the next generation, there are too many in our population and not enough food, so the population dies off a bit. This is actually stable behavior, and is seen in some bacteria cultures!

If we keep increasing r, this two cycle becomes a four cycle, then an 8 cycle and so on. Before we examine this, lets first take a look at a nice way of seeing this visually. What we are doing here is taking a point x1, evaluating x2 = f(x1), then x3 = f(x2), and so on. If we plot (x1,x2), this is a point on the logistic curve. Drawing a horizontal line to (x2,x2) gives a point on the diagonal line. To get back onto the logistic curve we draw a line to (x2,x3), then back to the diagonal line at (x3,x3). This probably seems like a strange way to see the logistic orbit, but if you experiment with it, you can see stable fixed points, stable cycles and anything else this equation may hide very easily. Here is a java applet that allows you to do just that. These plots are called cobwebs, (for reasons you will see shortly). Experiment with r=2.9, and r=3.2. You will see the fixed point and the two cycle that were covered earlier. The applet is used by setting the value of r in the 'r' text box. The other two text boxes, start cycle number and end cycle number, allow you to calculate a number of initial cycles, to let any messy parts of the cycle die out before the applet starts drawing. If start is 300 and end is 600 you should get a pretty neat picture of the cobweb. If you want to see the orbit right from the beginning, set start to 0. Initial x is the starting point of the cobweb.

Now that we have cobwebs under our belt, we can increase r further. If you didn't try increasing r past 3.2, try it now, try r=3.5 then r=5.65. You will see that the cycle has changed to a 4-cycle then an 8-cycle. These changes are called bifurcations. At a bifurcation the system undergoes a massive change in long term behavior. As r is increased, the bifurcations come faster and faster, until finally at about 3.5699 the cycle length becomes infinite. If r is further increased from 3.5699 up (but still below 4.0) then the system no longer has a cycle, it bounces about forever, but never repeats itself. Here is a cobweb for r=3.9.

This behavior is chaos. There is another way to easier see these bifurcations. If the stable points, or stable cycles are plotted as a function of r, then each of the cycles can be seen bifurcating into a cycle twice as long. After r is increased past 3.5699, chaos appears, but there are windows of periodic behavior interspersed with the chaos.

This route to chaos is called a period doubling cascade. It appears in many real life systems and very closely resembles this map. This is known as universality, the same simple map appears over and over again in just about every type of chaotic system. >>

(c) Blair Fraser, 1999


99.48.12 Pyramid-like structures (MetPhys) 

From: MetPhys@aol.com
Date: 12/11/01
Subject: Pyramid-like structures



I found certain "pyramid-like structures (which) might possibly correspond with the center of the radiating GOES ring", from cyberspaceorbit.com

Can you get a fix on the location as a valid ASM Grid Point?



99.48.13 Stonehenge, Grids and Particle Accelerators (MetPhys) 

From: MetPhys@aol.com
Date: 12/11/01
Subject: Stonehenge, Grids and Particle Accelerators


Home by Vind

Interdimensional Physics and Alphanumerics by Vind

Gary, Mr. Vind is another person who thinks Alphanumerically. You might like corresponding with another who thinks as you do, since you are a cooperative person. I would like to see you and Mr. Vind post email to my site archives after he studies the works of the other posters. It may prove enlightening.

To All, Mr. Vinds thought processes are simple but insightful when coupled with alphanumerics, which is just what we need. Please excuse the spelling and the seemingly disjointed clipped-sentence-summaries which may throw you off a little.

Pertaining to Stonehenge: I arranged a short table of the first, second and third powers of the circle numbers as follows:

Reference page:


^1      ^2      ^3

4.5     20.25    91.125
15     225     3375
32     1024    32768
55     3025    166375
84.5    7140.25   603351.125
120    14400    1728000
162    26244    4251528
210    44100    9261000
264.5   69960.25   18504486.125
325    105625    34328125
392    153644    60228448
465    216255    100558575

Do you see any exponential power numbers listed above which reflect the numbers that you all have worked with? I noticed 14400, 26244, 153644 and 216255 right away.



99.48.14 Iranian Mars Face? (MetPhys) 

From: MetPhys@aol.com
Date: 12/15/01
Subject: Iranian Mars Face?


Page 48

Sections List- 99 Electrons and Mythologies
Impossible Correspondence Index

Copyright. Robert Grace. 2001