Early Reflections on Crop Circles
These pages contain my early work on crop circle geometry and crop circle reconstructions.
My later work can be found on my website Crop Circles and More

  Geometry | Reconstructions | Crop Circles and More
 

Crop Circle Geometry - 3 D crop circle models

           
 
Making (two-dimensional) crop circles into three-dimensional 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.
 
 


Hackpen Hill, 1999

 
 
Next is the stamp to create the 1999 Cherhill formation.
 
 


Cherhill, 1999

 
 
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 three-dimensional. 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 three-dimensional shapes of the crop circles, though the stamps do look nice.

 
 
A more sophisticated way is to make 'real' three-dimensional 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 cross-section of the three-dimensional 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 cross-section 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 cross-section of such a three-dimensional 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 three-dimensional 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 nine-pointed 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 cross-section 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 nine-pointed star are interlocked in a peculiar way. My three-dimensional 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 three-dimensional 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 top-view of the finished model.

 
       
 
The image on the right shows the model in 'full-flight'. Notice how the tips of the tetrahedrons are, like with the Cherhill model, sticking out the surrounding sphere. A cross-section 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 three-dimensional representations of the crop formations. They are translations of two-dimensional crop shapes into the three-dimensional 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.