We construct four interlinked Vesica Pisces formations around a circle as shown. Their radii will then be 2 times that of the centre circle, with each arc intersecting the centre circle one quarter of the way round. If an outer circle is then put through the intersection points, this outer circle will be a bit less than double the radius of the inner circle. 
 

 A sixfold design was inscribed onto this template by the Circlemakers. Here is a different one, to give an idea of how it works. The wheat field allowed no access to the centre or even near it for construction. Only Steve Alexander flew over and photographed it, during the few brief hours of its existence. Allan Brown then discerned and drew its underlying structure.

792 squares were left standing, and this gives the /2 ratio when divided by 504, the total number of laid-down squares. The figure – kindly supplied by Allan Brown, from his book-cover – indicates how these laid-down squares could be counted. That ratio is within 0.04%, which is precise enough to look intentional. It would be less exact, had one more or less tuft remained standing. We are here dealing with a multiple of the basic 22:7 pi-ratio. The number 5040 is mentioned and used in Plato’s ‘Laws’ as having an ideal meaning, and the authors of Crooked Soley found this to be relevant. 

Note that the outermost part of this pattern is hardly ‘formatted’ with squares. The best and only published image is that published in Crop circles, Signs, Wonders and Mysteries by Steve and Karen Alexander 2006, p.181. However, from this writer’s special request, Steve most kindly dug up another image from his fly-over, taken at a better angle than that published, and here it is! This is a close enough resolution to see that the ‘slices’ do not all have the same thickness. However it does look like an exact 2:1 ratio between inner and outer circles, which is problematic for the analysis given here. 

Braid Pattern – South Field, Alton Priors, Wiltshire 8 August, 2003 

A braided pattern was woven on a square template. The same pattern, half-size, then spiralled in towards the centre, in eight braids. The construction design given by Ohayv may not be very credible, and we here prefer the indications given by Allan Brown. 

A Vesica Pisces design has circles of half the size packed inside, as shown. Let us suppose that the pattern unfolds with all of these small circles thus touching. An interlinked sequence of Vesica Pisces at right angles to each other is thereby constructed. In this diagram, the yellow-coloured small circles represent the flattened wheat, while the others merely define the pattern. The pattern of wheat left standing is shaded in red. 

Outer and inner boundaries are constructed around this iterating pattern, their widths being intervals inherently present in the design. Taking the small circle diameter as unit measure, the interval between flattened wheat circles (yellow) is 2-1, and this gives the outer band thickness. There are smaller gaps between the larger circles, equal to 5-2, and these define the thickness of the inner boundary. Thus the decorative art of the Circlemakers emerges from a sense of delight in the maths, whereby they wanted to give expression to key ratios inherent in this Vesica-Pisces pattern. 

At the centre of this design lie eight small circles having prominent central tufts of wheat, marking out a circle identical in size to these Vesica-Pisces circles, whereby the outer and inner designs reflect each other.

The outer boundary is constructed by enlarging the upper set of large circles on our diagram by 2, doubling their area. Thereby a further set of ‘Vesica Pisces’ appear. There are fifteen Vesicas present in the construction matrix for each side of the big square. These extra large circles are now eight times the area of the little circles. Some part of this iterating design might be used decoratively, eg on a subway wall? The entire matrix would have to be in place before any wheat could have been laid down. 

An interlocking geometric matrix underlies this pattern, suggesting the existence of an advanced but little known school of decorative art, having a subtle understanding of the Principles of Harmony.