





In the mid 90s some of the
found crop circles were based on fractals. For instance the socalled 'Juliaset'
at Stonehenge in 1996 and the 'Triple Juliaset' at Windmill Hill the
same year. Or the Kochfractals in 1997. In later years, this resembling
disappeared and was replaced by other features. In 1999 many of the crop
circles looked threedimensional. But did the fractals really disappear? 



West Overton  England 1999




If you make a drawing of the 1999 West Overton formation, cut it out and fold it
together, you get a threedimensional shape: an octahedron. See image on
the right. This octahedron forms the core of a threedimensional fractal.
To understand this we shall first have a look at an other Platonic solid;
the tetrahedron. See image below. 








By taking a second tetrahedron and putting it upside down 'in' the first
tetrahedron, we get a socalled startetrahedron. See image above. The
image on the left shows this startetrahedron viewed from above. 



When we take this startetrahedron and 'pull out' the red tetrahedron, we are left
with a tetrahedron with its 'heart' taken out. See image on the right. The
empty space in the tetrahedron is where the two tetrahedrons were
overlapping. 







This empty space we can fill up again. See image above. If we just look at the
shape of the fillingup material, we see an octahedron! With other words:
the heart of a startetrahedron is an octahedron. See images on the right. 





The image on the left shows the tetrahedron with the filling. You are looking
at one side of the tetrahedron. All the other sides look like this. What
we see is an upside down red equilateral triangle (=octahedron) in a
bigger equilateral triangle (=tetrahedron). 



We can repeat the same procedure with the three green equilateral triangles,
which are in fact three tetrahedrons. The image on the right shows the
result. We are now looking at the second step of the iteration that forms
a Sierpinsky Gasket, which is a wellknown fractal! 




The procedure described above can be repeated again and again forming a
threedimensional Sierpinsky Gasket. A true threedimensional fractal!
Remember: the red fillings are in fact octahedrons, the shape formed by
folding together the West Overton 1999 formation. 






So the fractals did not
disappear, at least not up until 1999. They were just hidden. And more: they were hidden in a
threedimensional form! 











