Posted by Michael Glickman on May 22, 2012

VIRTUAL PAIRS
There were two sibling sets, pairs or virtual twins which occurred in consecutive years, 1998 and 1999. The first pair, Clatford and Furze Hill explored the circle while the second pair, Windmill Hill and West Kennett dealt with squareness.
These sets shared a specific and unique characteristic. The standing part of the design in one formation was laid down in its sibling and similarly, the laid crop in the first was switched to standing in the second. This had not happened before or since and while, as usual, I can draw no conclusion from these events, I feel they should be considered.

Fig.1 - Clatford, 21st June 1998

June 21st was a very hot day and it was a long hike up a deceptively steep slope to the formation. The formation was precisely laid and very impressive but I confess that, after the exhausting climb and under the heat of the south-facing slope, I failed to spot the simplicity and magic of the geometrical scheme until later.

Fig 2 - Basic geometry of Clatford

Please take a moment to consider this carefully. The diagram is remarkably simple and logical in its construction yet it produces a form both beautiful and precise. It leaves no room for manoeuvre. This might be an appropriate time to refer back to The Lobsters of Honey Street February 27, 2012. Figure 4 of that blog shows how the individual Lobster element is based on the same fundamental diagram.

Fig.3 - Developed geometry of Clatford

There was to be a further astonishment the very next day, 22nd June 1998.

FURZE HILL
At Furze Hill, slightly over three miles to the southwest of Clatford, a virtual twin of the Clatford formation appeared [Fig.4]. It lay in a field adjoining the Wansdyke, an ancient defensive moat-and-mound system that runs for miles across the Wiltshire Downs.

Fig.4 - Furze Hill, 22nd June 1998

Fig.5 - Developed geometry of Furze Hil

Furze Hill was based meticulously on the four rings shown in figure [Fig.2] but, in this case, as figure [Fig.5] shows, different zones were selected for flattening.

A MINOR REVELATION
I was fortunate in being able to visit each of these crop circles on the day of their arrival. This was entirely accidental. I was unaware of their importance at the time and it took me months to understand the significance of their relationship.

The simplicity and economy of the design of the formations is impressive but, perhaps their similarity is even more remarkable. With the exception of screamingly obvious candidates such as simple circles or quintuplets I cannot recall any two previous formations, which were so precisely twinned. Their arrival on consecutive days, their location on south facing slopes but above all their shared geometry and scale lead me to a surprising conclusion. The Clatford and Furze Hill crop circles of 21st and 22nd June 1998 should not be considered as two formations but rather as a unique crop circle event.

I feel certain that this could be a small step in the right direction but it still leaves me perplexed. These formations (or this event) was related, above all, to the vesica pisces. Perhaps there are clues there.

THE SYMBOLISM OF THE VESICA PISCES
Sacred Geometry is said to express man’s efforts to understand and symbolise the connection between the Worldly and the Divine. Just as the square is held to represent the world and material reality, the circle signifies God, All-that-is and the Spiritual Realm.

Fig.6 - Vesica Pisces with two equilateral triangles

It is difficult in a few words to convey the richness of symbolism and metaphor of the Vesica Pisces. Everyone should get a compass and familiarise themselves with these
exercises.

It is clear that the authors of the crop circle phenomenon are as familiar with and as thrilled with the Vesica as are we.

THE SECOND PAIR
During the following 1999 season there were two formations which shared some of the remarkable characteristics of the 1998 Clatford/Furze Hill duo.

First, at Windmill Hill on 16th June 1999 [Fig.7] an elegant and enigmatic formation appeared. A square decorated with many precisely organised small circles was contained within a large circle. The arrangement of the small circles, though clearly very deliberate and meaningful, was difficult to comprehend.

Fig.7 - Windmill Hill, 16th June 1999

Fig.8 - West Kennett, 4th August 1999

The West Kennett and Windmill Hill crop circles were about 2 1/2 miles apart and, like the Clatford/Furze Hill siblings they had similar geometries with laid down crop becoming standing and standing becoming laid down.

Fig.9 - West Kennett showing fractal

Only three “Granddaughters” are manifested. The fourth red-framed square was not there and is shown here in diagram [Fig.9] only as an illustration.

This system could, in principal, continue forever, diminishing to sub-microscopic levels.
It is a fundamental of fractal systems that they are without scale. That is, they have the ability to grow or to shrink infinitely simply by reiteration. The West Kennet crop formation performed three iterations, (mother to daughter to granddaughter) but the fourth iteration, which should have been an even smaller square, becomes a circle at each corner of the red, granddaughter squares.

This is entirely consistent with the Silbury Hill and Milk Hill triangle-based Koch fractals of 1997. They, too, went through three repetitions and, for the fourth iteration, displayed a circle where the triangle should have been.
There is a reason for this. The medium, growing crop, can only show a certain level of detail. It could be argued that wheat could not be manipulated to display triangles or squares at the small scale required. The pixel size of the medium is too coarse.

A CONCLUDING CONUNDRUM
We have seen that a fractal is able to grow or shrink infinitely. We have seen that crop circle fractals are constrained only by their medium and cannot make smaller signs.
But what stops them getting bigger? Perhaps the real constraint is no more than the limit of our vision. Perhaps we can only digest four iterations. Maybe the West Kennett crop circle was largely invisible to us but was, in reality, as big as Wiltshire, or England or Europe. Perhaps what I called the Mother square was truly a great, great granddaughter…

Acknowledgements and thanks
Photography: Steve Alexander
Diagrams and graphics: Ofmil Haynes Jr