Strange Attractor Crop Circle
 Formation and the End of Time  

By Joseph E. Mason

"The Strange Attractor" Crop Circle Formation
Hackpen Hill, Wiltshire
August 18, 1997
Photo: Steve Alexander


On July 31, 1990, I began to write about the symbolism of the Mandelbrot Set. I continued to write about symbolism involving various parts of chaos theory. This seemed quite odd, even to me, but such things are part of my experiment. I simply record various ideas that come to me, without questioning how odd or silly they may be. So often, they lead to strange "coincidences."

I sent some of the ideas to various people over a period of several years, including crop circle researcher, Pat Delgado. Unfortunately, Pat did not have time to read much of it. Some of the material I sent to people included information about the Mandelbrot Set, Julia Sets and Kotch fractals, which are snowflake-like.

On August 11, 1991 some thirteen months after my speculations, the Mandelbrot Set crop formation appeared. In 1996 a Julia Set spiral formation appeared next to Stonehenge and a Triple Julia Set spiral appeared. In 1997 three Kotch (snowflake) fractals appeared:  

The Koch Snowflake Fractal at Silbury Hill

The complex Kotch Snowflake fractal at Milk Hill, near Alton Barnes

The Kotch Fractal-Like Triangle at Hackpen Hill (Strange Attractor)

These shapes are all related to Chaos theory.

Around 1992 I had a dream of a man becoming more and more fearful. A voice said, "You have just witnessed bifurcation into new species of fear."

Chaos Theory

I first learned of Chaos Theory around 1987, when I listened to a TV interview with James Glick, who wrote a book on the subject. I later purchased the book, Chaos: Making a New Science, by James Glick (Penguin, 1987. New York). I found a site on-line that has a brief description of Chaos Theory:

Honors 183: Chaos Theory: The Making of a New Science

Here is an excerpt:

"Chaos Theory" (Nonlinear Dynamic Systems) is a collection of concepts and phenomenon that have been recently observed, or successfully applied, throughout the natural and social sciences. Consequently, scientists' understanding of deterministic systems has been altered, and unexpected regularities have been observed across a wide range of natural domains, for example, physics (turbulence), physiology (neurological processes), chemistry (reactions), biology (structure and growth), and economics (stock market behavior)."

The site has links to other information about the science of Chaos.

It is said that this new science is one of the most important scientific developments of the twentieth century. Prior to its discovery little was known about complex, or nonlinear systems. Almost everything in the universe is complex, so the new understanding is quite important. This includes human brain function.  

Part of the new science involves producing diagrams on the computer monitor. Programs are writen involving mathematical computations, which place pixels (dots) on the screen at exact locations (and sometimes in various colors) resulting from the computations. Some of them are quite beautiful (See note 1).

In my on-line surfing, I found a site that expresses views similar to my own, that is, Chaos theory may also have a spiritual meaning -

Fractal Chaos Crashes the Wall between Science and Religion

Geoff Stray's Article

On December 12, 1997 I received issue #71 of SC Magazine. I found Geoff Stray's article, "Hieroglyphs of Dimensional Interface," quite interesting. He speculates on "the end of linear time."

Geoff points out that the most enduring feature of the crop formations is the circle, and that circles suggest rotation and therefore cycles of repetition. The circle defines the movements of the Earth around the Sun which can be multiplied into cycles of time.

Quintuplet Set crop formations began to appear in 1978 and continued into 1997. The shape is similar to planets around a sun. Geoff noticed that they are also similar to the Aztec Calendar Stone, which depicts five ages called, "Suns." (I sent an Aztec Cosmogram with this information to crop circle researchers about six years ago). The central sun in the depiction is the "Fifth Sun." It is surrounded by four previous Suns, which were ages that ended in cataclysm, when the magnetic field of the Sun reversed, according to research by Maurice Cotterell and Adrian Gilbert. (The Mayan Prophecies, Element Books Limited, Shaftesbury, Dorset SP7 8BP (England, 1995)

The Mexican UFO wave, says Geoff, started on the day of the solar eclipse in July 1991, complete with "corn-on-the-cob-circles." Britt and Lee Elders correlated 1991 to the end of the Fifth Sun, but other researchers say it will end in 2012, when the Mayan calendar ends.

Photo: Steve Alexander

In "SC" # 68, Michael Glickman interpreted the 1997 Etchilhampton "Gird" crop formation (above) as a pointer to 2012. The formation was a 30 x 26 checkerboard-like grid, giving a total of 780 squares. This, Michael theorized, could indicate the thirty 26-week periods between 1997 and 2012.

Geoff adds that the 780 squares of the grid are exactly divisible by the TZOLKIN, or Mayan Sacred Calendar, which is a grid of 260 squares with sides of 13 x 20. Three Tzolkins fit into the crop grid pattern. Two fit straight in and the third after bisection.

The grid seems related to a "map" called "Psi Bank Warp and Holonomic Woof" mentioned in a book called "Earth Ascending," by Jose Arguelles (page 121). The "map" consists of eight Tzolkins joined together showing relationships between the Mayan calendar, the "I Ching" and the 64 DNA codons. Arguelles researched the Mayan calendar, physics, philosophy, geomancy and the "I Ching," and concluded that mankind is creating a "noosphere," or mind layer, around the Earth, which is evolving towards the "Omega Point of Planetary Awakening" in 2012, according to Teillard de Chardin. (This may fit with some coincidences I had in 1990, concerning a Saturn-like spiritual ring around the earth).

When "Earth Ascending " was published in 1984, Arguelles was unaware of a book published in 1975 called, "The Invisible Landscape," by the McKenna brothers. The book gives a mathematical analysis of the "I Ching," concluding that the 64 hexagrams of the "I Ching" oracle, or "Book of Changes," was originally used as a calendar portraying 64 timewaves which interact to form a "modular hierarchy" of 26 levels. The modular hierarchy is a Mandelbrot fractal where each of the levels is 64 times greater than the one below. Mapped against history, the "end-of-time" climax, where the waves all peak together, was found to be in the year 2012. At the time, the McKennas were not aware that this is the end of the Mayan calendar!

Geoff says that the Mandelbrot crop circle formation also illustrates the modular wave hierarchy encoded in the "I Ching," and this suggests our imminent encounter with this unseen dimension in 2012.

About a month before the Mandelbrot Set crop formation appeared, there was a report of a triangular "craft" and balls of light over Barbury Castle. That night, the famous triangular formation appeared at that location. According to Geoff, the design has been called, "The Alchemical version of the Mandelbrot Set." It therefore may imply the End of Time in 2012.

Jon King, editor of "UFO Reality" magazine, had a strange extra-dimensional experience in 1980. He became convinced that a large triangular area of the West Country is a type of dimensional gateway. In 1986 he published a booklet about it called, "The Aquarian Triangle" (Most of the corp formations have appeared in the "Wessex Triangle"). He wrote that this triangle would soon be the recipient of "light codings" or "energy codings" that would be followed by human interaction with the creators of the codings. In 1989, Jon went with some friends to Barbury Castle, the exact center of the Aquarian Triangle, and performed a ceremony visualizing the "mothership" landing there. Two years later, the triangular formation appeared at the site. Its shape is almost identical to the Aquarian Triangle. (see note 2)

Jon published a version of the schedule given to him in the "TUMI" column of "UFO Reality," #4. It gives a timetable of events in the forthcoming dimensional shift, culminating in a dimensional interface in 2011, decloaking in 2012, and Earthshift in 2013.

Geoff reviewed the various crop formations associated with chaos theory, as mentioned in the beginning of this article. The final formation of 1997, he says, was the "Strange Attractor" fractal at Hackpen Hill . A photograph of the Strange Attractor crop fomation is at the top of this page.  The term means "an irreducible invariant set that attracts the trajectories of all nearby points." This term was used by Terrence McKenna to describe the "Omega Point," which sucks our evolutionary trajectory towards it, like the plughole at the end of time.

Many have pointed out that the last crop formation of a season is often the most, or one of the most, important. Some believe the final formation gives clues as to the formations that will appear the following season.

Geoff is currently working on a theory correlating information about sunspot cycles, and reversals of its magnetic field. The reversal point is thought to be approaching in 2012. According to Geoff, the sunspots are thought to have an effect on the endocrine glands of human beings, which relate to the chakras (see notes 4 and 5). Geoff is also working on esoteric use of endocrine products and ancient Egyptian techniques of arousing dormant functions of endocrine glands to produce a fourth-dimensional body.


Hieroglyphs of Dimensional Interface
by Geoff Stray

The number 26, The Mayan Tzolkin, and the Grid Crop Circle
(a related article)

The Butterfly Effect
by Dee Finney

The Butterfly Effect Crop Circle Formation of 2007

DNA Connections
DNA Repair, Dreams and Crop Circle Formations

2012: Dire Gnosis - by Geoff Stray

The Mathematics of Chaos

Julia and Mandelbrot Sets

All About 2012

Differences in the Squares of Mirror Numbers


1. For some very beautiful fractal art, take a look at --

Carlson's Fractal Gallery

2. I wrote about some of the angles in the Barbury Castle formation, and how they are suggestive of six ages, with a big hint indicating the end of the age of Pisces and the beginning of Aquarius. It seemed to be "coincidently" supported by a dream of my friend Jeff. See -

The Pleiades and the Seventh Ray on the Seventh Day

5. I wrote an article about the chakra connection to the crop formations at --

Crop Circle Formations As Chakras

Update note, 14 January 2008

It has been over six years since the last update of this article. Recent events and information indicate that the concept of the "noosphere," mentioned in the above article, is being confirmed. The evidence is massive and complex, in my view. Many dreams, crop circles, myths, and religions connect with the idea in various ways.

The meaning is related to the idea of Communion, but not in the traditional sense.


8 Jan 2008, 1:11 PM

This e-mail is coincidental with the above, about the spiritual ring around the Earth. This is a paste of that line --

<< The last line of the song above ("When God left the ground to circle the world") indicates that the spirit of the Demiurge Christ encircling the Earth, like the "Saturn- like" rings . . . actually a sphere around the Earth.>>


Subj: Fwd: Dreams
Date: 1/8/2008 10:53:53 AM Pacific Standard Time
From: Dee777
To: JMason4557


Forwarded Message:

Subj: Dreams
Date: 1/8/2008 10:33:32 AM Pacific Standard Time
From: nue

I can sense the hidden meanings in movies - How they know something we do not. In I am legend the theme is bio-warfare - when trying to cure cancer? Now that scientist are finding new discoveries on HUMAN dna (genome project) - One can literally take out audio clips from movies and play it with video of LIFE events... MY dream is to create such projects.

The noosphere is the grid we are manifesting with peace, love and harmony. Those who try tell put us  in fear of are losing a grip as our numbers continue to grow. The Golden Age, Age of Aquarius - 2008 is the year light-workers start to come out.

"The beast runs AMOK in my Kingdom" Was the call sent out by mother earth - Starseeds/lightworkers came in numbers and now have awakened . . .

In love and Light nue!


Iron & Wine - Boy With A Coin

A boy with a coin he found in the weeds
With bullets and pages of trade magazines
Close to a car that flipped on the turn
When God left the ground to circle the world

A girl with a bird she found in the snow
Then flew up her gown and that's how she knows  
That God made her eyes for crying at birth
Then left the ground to circle the Earth

A boy with a coin he crammed in his jeans
Then making a wish he tossed in the sea
Walked to a town that all of us burn
When God left the ground to circle the world


Comming soon

Communion 2012
The Stunning Noosphere Meaning  
The Cosmic Christ Consciousness Rings the Earth

If you would like to ask questions or make comments about this article, please e-mail Joe Mason at

This page was originally created in 1997

This page was last updated April 7, 2008

This prvious update was September 26, 2001

The URL of this site is: