
What are crop circle reconstructions?

Crop circle formations appear in various "flavours", from quite uncomplicated single circles up to very complex patterns. See for instance the very interesting 2000 Chilbolton Radio Telescope formation. A reconstruction is made to better understand the design of the pattern. It is a drawing of the floorplan of what has been found in the field. Although very exciting to know, my reconstructions are not meant to find out how crop circles are created in the fields. Who follow my reconstructions will discover that, at the end, superfluous parts are often removed, and it can of course easily be seen, that in the field, this is completely impossible! There are – at least – two ways to make such a reconstruction. The first is to make measurements on the real formation and then make a drawing that matches these measurements (on scale of course) as accurately as possible. In stead of the real formation, an aerial image can be used to do the measurements, but then special attention must be given to the perspective deformation and the influence it has on measurements.


The second is the one I prefer. It is not only based on measurements, but goes one step further. It tries to find the relationship between all the constituent parts of the formation. Many patterns of crop circle formations show such an intriguing internal coherence that it invites, so to speak, to be discovered. "Rulerandcompass constructions" are found to be very suitable for these reconstructions – literally.


What are rulerandcompass constructions? In contrast to making use of a ruler with divisions to take the measure of things and express it in metres or feet, rulerandcompass constructions only use undivided rulers and compasses. Not all patterns can be constructed by (strict) rulerandcompass rules. For instance, a regular heptagon – 7sided polygon – can not be constructed in this way. See the
rulerandcompass constructions page to learn more. There are, however, other ways of constructing oddnumbered polygons. Refer to the non rulerandcompass constructions page.


How are cropcircle reconstructions worked out? Usually, it takes a number of steps. First, I use MS Word, insert the aerial picture as a background image and draw ellipses and lines over it as accurately as possible in accordance with the pattern. This helps to get an idea about the internal relationships, and to have a means to make measurements. 
photo by: Steve Alexander 
If perspective deviation is not too large, lines remain lines and circles become ellipses. Except for the very large ones: large circles become distorted ellipses. (Imagine you fly not too high above a very large circle, right above one edge. That part of the circle remains circular, since you are straight above it. But the far edge at the other side you will see very skewed, and thus will look like an ellips. And ellipses can not have an elliptic and a circular part at the same time). Take a proof: print a circular formation with a clear center, for instance the 2001 Folly Barn formation (the aerial picture above, or better still the other one taken by Steve Alexander at the same Crop Circle Connector page). If there were no distortion, a circle would become a nice ellips with the circle's center at the center of the ellips (the intersection of the axes). But here not so; the center is above the middle. Turn the print upside down and you will see the difference! That makes it tricky to use aerial pictures for measurements.


The reconstruction itself is done in AutoCAD. AutoCAD is perfectly suited for doing rulerandcompass constructions, despite the fact that, internally, it works completely numeric. For construction purposes, it allows for using all sorts of special points (which are calculated with very high precision), like intersections, centers, tangent points, endpoints, middlepoints, etc. All these points do have rulerandcompass counterparts. 
In the first reconstruction trial, I often mimic the measurements, in order to find special points that coincide with the measured ones. When good candidates are found, I start the strict rulerandcompass construction. If successful, this leads to a complete diagram of the formation.



Then, a difficult step follows. The matching. In my opinion, this is an important step. The better the result of the reconstruction matches the original picture, the better the "proof", that this is indeed the reconstruction! But unless we learn to know the meaning of the originators directly (whoever they may be), a real proof will it never be. (By the way, I doubt at all if – objective – proofs really exist, see the propositions with my thesis). There are a number of difficulties here. First the assumption, that the patterns in the field have been created according to a design. And that this design is a geometric design, not just a freehand style of art. Next, that this design has led to a realisation with a certain accuracy. Some crop circle formations show a much higher regularity than others. Then again an assumption, that the patterns can be reconstructed (and thus are constructed in the first place) by rulerandcompass rule (apart from the exceptions that exist for this rule). 
photo by: Steve Alexander 
The match itself is carried out with yet another program, 3DStudioMAX. The aerial image is used again as the background image, and the geometric drawing (exported from AutoCAD) is imported and layed over it. Then, an elaborate part of the work begins! I mean, changing "position", "elevation", "rotation", "zoom factor", "viewing angle", "distance" of the drawing in 3D all in close cooperation! If, in the end, the reconstruction really matches (and some perfectly do! for instance, the Folly Barn formation above), then the strong feeling of "yes, this is the good one, I found it!" results.


Copyright © 20012002 Zef Damen, The Netherlands

