








Making (twodimensional) crop
circles into threedimensional shapes can be done in various ways. It
all depends on the conventions you make before you start. The simplest
way is to make a stamp, which can be used to press the shape of the crop
circle into the crop. Off course you won't get any nice lay, but you
will at least get the shape down. Here under are a few examples given of
such stamps.
The first stamp shown is the one you need to make the 1999
Hackpen Hill formation. 






Next
is the stamp to create the 1999 Cherhill formation. 






The
third stamp is to produce the Winterbourne Bassett formation of 1997. 



Winterbourne Bassett, 1997
Photo: (c) Steve Alexander









As you can see, the stamps are
really threedimensional. They have, beside length and width, also a
certain thickness. This can very well be seen at the image on the right.
But to be honest this is not an elegant way to make threedimensional
shapes of the crop circles, though the stamps do look nice. 




A more
sophisticated way is to make 'real' threedimensional bodies. With this
we have to make a few agreements. For example: a sphere will represent a
circle. The formation itself will be represented by a crosssection of
the threedimensional body. Now, this is not easy. What to do for
example with a triangle? There are at least two options. We can use a
huge tetrahedron. A crosssection of this tetrahedron will produce an
equilateral triangle. But we can also use two tetrahedrons with their
bases stuck together. In this way, we have the same shape 'above the
field' as 'under the field'. A crosssection of such a threedimensional
body will produce two separate bodies. The one body is the mirror image
of the other body. This feels for me the best and this is the way I
constructed my threedimensional bodies.
Lets have a look again at the 1999
Cherhill formation. 




I first constructed a body that
represents the centre of the formation. It consists of six paddles. Each
paddle is created by two spheres. The spheres were interlocking and then
a Boolean operation was performed. In this way, each paddle is thicker
in the middle then on the outside. 





I treated the ninepointed star
as three separate equilateral triangles. So, I constructed three sets of
two tetrahedrons each. The two tetrahedrons in a set were constructed
base to base like explained above. 







A sphere surrounds the whole.
The end result can be seen at the image on the right. A crosssection of
the body on the right will (nearly) generate an image identical to the
1999 Cherhill formation. Nearly, but not 100% exact. If you take a good
look at the formation, you will see that the three triangles that form
the ninepointed star are interlocked in a peculiar way. My
threedimensional model does not generate this feature. 




The formation that appeared in
1997 near Winterbourne Bassett is an other of which I tried to make a
threedimensional model. 




A solid sphere, with another
'hollow' sphere around it, forms the centre of the formation. The
triangle is again a set of two tetrahedrons. Three hollow spheres
construct the circular elements at the side of the formation. A sphere
surrounds the whole. The image on the right shows a topview of the
finished model. 








The image on the right shows
the model in 'fullflight'. Notice how the tips of the tetrahedrons are,
like with the Cherhill model, sticking out the surrounding sphere. A
crosssection of this model will again not generate a 100% correct image
of the Winterbourne Bassett formation. The formation it self consists of
alternating patches of flattened crop. My model is not capable of doing
this. The model is still a very good representation of the actual
formation. 




I realize that it is quite
unlikely that models like I constructed them are actually the shapes
that create the crop circles. The models should be considered as
threedimensional representations of the crop formations. They are
translations of twodimensional crop shapes into the threedimensional
world. Perhaps somebody recognizes the models. Perhaps the models look
like representations of some chemical compound. Please let me know if
you do recognize them. 

















