The apparently random positioning of visitors photographed in a crop circle in July 1998 now reveals a set of geometric characteristics too precise to be glibly written off as coincidental. It is my view that these discoveries are momentous. They demonstrate inarguably what researchers have suspected for many years: the crop circle phenomenon demonstrates an as yet inexplicable, but now undeniable, interactive connection with people.

The Background

On the 23rd of July 1997 an enormous and elaborate formation was found in a wheatfield close to Silbury Hill in Wiltshire (1). The hill is a striking conical mound, the largest man-made earthwork in Europe which is one of the centres of English crop circle activity. The crop circle, almost 250 feet in size, had the largest ever single area of laid crop (approx 0.85 acres), a record it was to hold until the arrival of the huge 1.6 acre heptagram in East Field in July 1998. Popularly called the Silbury Star, the formation was in fact an accurate rendering of the Koch fractal, a mathematical protocol discovered early in the century by mathematician Helga von Koch.


Image No. 1 • ©1999 Patricia Murray

The Koch Fractal

The Koch fractal is constructed according to a formula of great simplicity. An equilateral triangle (3 sides of length L) has each of its sides divided by three. A second, smaller triangle of size L/3 is placed at the centre of each side of the first triangle. Each of the sides now has four surfaces of length L/3, making a total length of 12 x L/3. Each of the twelve surfaces is then divided into three and a third, yet smaller triangle is placed at the centre of each surface. The size of the third triangle is L/9 and there are now 48 surfaces of the smaller length.

The interest of this early fractal system is that it can increase infinitely by this iteration. The perimeter length will grow without limit (in tiny increments) but the area will never extend much beyond the initially established boundaries. We are presented here with a mathematical paradox which shows the way that infinity may be contained within a limited area.

The Koch system has been overlaid on the aerial photograph (2). It is clear that, in this crop formation, only three triangular iterations were carried out, shown here in black, blue and red. At the fourth level, the triangles become circles! While I have no explanation for this, it should be noted that the circle diameter is 1/3 the size of the third series of triangles. That is, while the shape has been abandoned, the sequence of dimension has been respected.


Image No. 2 • ©1999 Patricia Murray

The Photography

Some days after the arrival of the Silbury formation, Patricia Murray went on a photography flight. She covered several formations and then flew towards Silbury. As she approached, she was delighted to find a ring of people, presumably meditating, in the formation. This is a rare circumstance. There are many photographs of people in formations but, to my knowledge, a formal ring has rarely - if ever - been recorded. The brief time the group spends together has never coincided with the brief aerial passage of a photographer.

When Patricia landed, she was in a state of great excitement. She had noticed the ring as she approached Silbury and was certain that the energy of the meditating group was tangible in the plane.

Crop circles - the designs - are amplifiers in a sense. From many hundreds of feet up, you could feel that group of people. she said later. When the slides were developed it was clear that she had recorded a unique moment. The ring of meditators in the Silbury Fractal was included as the November image in our 1998 calendar.

A Hunch

I have lived close to this image since it appeared and it remains for me one of the great crop circle photographs. It is on the wall of our office, beautifully enlarged and, of course, as I write, having just passed through November 1998, I have looked at it daily.

Patricia and I do a series of intensive workshops on Crop Circles, Sacred Geometry and the interactive nature of the phenomenon. In early December I had an intuition of enormous clarity. The geometric information in the circles is so dense and the interactivity of the phenomenon so profound that I suddenly knew that the ring must be precisely positioned.

The Position of the Ring

In the early '90s John Martineau's work demonstrated, among other things, the importance of the tangent, the straight line which touches the curve. I had no idea what I was to look for. Clearly the ring was not in the centre of the formation but I was certain that I would discover other geometric constraints and the tangent was the key. If the two central cross axes of the formation are drawn (3) the ring is seen to sit precisely into one of the angles, thus tangented by both lines. I have enlarged the ring and I have stretch-adjusted the photograph to bring it to an approximation of a vertical shot and thus to bring measured dimensions into parity. I have allowed for perspective. The axis lines are drawn at ground level, not crop height which is about thirty inches. Thus the ring is read where people are sitting, ground level, and not shoulder height. The accuracy of positioning is extraordinary. Please note that though everything was checked by me on a computer-stretched image, most of the images included here are normal photographs. Image (7) is the only adjusted figure included here.


Image No. 3 • ©1999 Patricia Murray

The Size of the Ring

The majority of the visitors to the formation have gathered and seated themselves in a circle of surprisingly accurate roundness. There are a few others in various positions not sitting in the ring. Remarkably, the diameter of the ring is the dimension of the third, or smallest triangles (4 & 5) approximately 26'6". Once again, though this is clearly discernible from the untouched photograph, the computer adjusted image allows direct measurement. This confirms that the diameter size and the triangle size are substantially equal.


Image No. 4 (left) • click on images for enlargements • Image No. 5 (right)

Positioning of Visitors

There are several individuals in the formation who are standing or sitting individually and not a part of the ring group. (6) shows a line drawn between two of them, Visitors A & B. It passes precisely through the centre of the ring. Though the precision of the line's positioning was rewarding I went further to hope that the line between would be divided by the ring into lengths which respected the Golden Section proportion, that is 1:0.618. My wish was optimistic! When measured on the corrected photograph the proportion was about 1:0.55, far from the Golden Section.


Image No. 6 • ©1999 Patricia Murray

Coincidentally, Patricia Murray was to meet Visitor B when she went to the formation the day after the flight to take ground shots. He approached her saying that he had forgotten his camera and would like her to photograph him in the formation. He gave his name and address in Brazil and asked her to send him a print. We would like to hear from any other people in the photograph and to investigate the circumstances further.

A Seven Pointed Star

The significance of the line between A and B is dwarfed by another discovery. This is shown on corrected photograph (7). Visitor A sits precisely at the point of a sevenfold star (or alternatively on the circumference of the circle which contains a sevenfold star). The sevenfold star contains the ring of people exactly. Sevenfold geometry has been awaited for some years and though it was hinted at (in the 1996 Oliver's Castle formation for example) it was not to appear until the summer of 1998 when we had four sevenfold formations. Seven represents the geometry of spirit and revelation.

If we assume that the circle containing the star has a diameter of 1 then the contained ring of people will have a diameter of 0.222. For comparison, a six-pointed star seated in a diameter 1 circle will contain a circle of diameter 0.5 while an eight pointed star will contain a circle of 0.387.


Image No. 7 • ©1999 Patricia Murray

A List of Curious Coincidences

1. The ring is positioned at a precise tangent to the two lines which bisect the formation.
2. The diameter of the ring is the size of the third, smallest triangles.
3. A line between A & B passes directly through the center of the ring.
4. Visitor A's position defines the perimeter of a circle, concentric to the ring of people. A sevenfold star constructed in that circle precisely contains the ring.

Several Hypotheses

I can think of four hypotheses, the first two of which will be immediately seized on by scoffers. They are as follows.

A. Coincidence
Those who wish to avoid looking at this will immediately dismiss it as coincidence. There are however too many synchronicities to allow us so easily to dodge the implications. To use Professor Hawkins phrase the impartial mathematics of probability are stretched here beyond reason. Even if one of the items is seen as coincidence - or two - then how do we explain the remainder?

B. Hoax
A second explanation would be that the whole event was orchestrated and directed by us or indeed by others. While this notion is almost too ludicrous to address, I would make the following points. First, I remained in the clubhouse at the airfield (which is one hour's drive from the location) throughout the flight. Second, neither Patricia nor I knew the order in which the formations were to be approached and photographed. Third, had it been hoaxed, why would we wait eighteen months to reveal it. If it was carried out by others, why have they kept silent? Fourth, given the nature of the circles and their tendency to be randomly visited by diverse people, the idea that this level of organisation could be achieved and kept secret is untenable.

C. Swarming
Work has been carried out in architectural academic circles which looks at patterns of crowd behaviour in large spaces. They contend that architectural form tends, in some as yet incomprehensible way, to influence the conduct of groups of people in built space. I will be sending my information to the authors of this work to see if they can shed any light on the subject in relation to crop circles.

D. Interaction
The visitors to the crop circle were in some way inspired, moved, motivated or encouraged to take specific positions in the formation at the very moment of the plane's passage.

Conclusion

Copyright © 2010 Tim Stouse
Last modified: December 10, 2010

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