They can't be called "hoaxers" if there's no real phenomenon to hoax. It's the audience, not the artists, that misidentifies the art as extraterrestrial or supernatural.

I'm confident the artists understand all this BS.

I remember the toy "spiragraph" that I had as a kid, I think a lot of the designs are a mark up of this in one ability of geometry... It's when I started seeing the insects and humming bird and such that I kind of lost interest... In the designs, I find them highly artistic no matter where they come from...

It's the simple crop circles that are a plain geometric desing that have the seeds altered genetically that make me wonder about some of them but I'm guessing that some university students could come up with something that could account for that but it still seems out there and I do like crop circles no matter where they come from...

For many years I knew a researcher into this type of unexplainable phenomena and unfortunately, those who wish to condemn it will continue to do so and produce debunker after debunker to back them up. One case I remember happened a few years ago now in a very public place and was video taped from the air.
It was on a paddock across the highway from Stonehenge one summer. A pilot who flew tourists over the site returned to his airport ten minutes flight away and refueled before taking his next group out. When he arrived at Stonehenge a very elaborate scorpion design was displayed in the field across the road. About the same size as the one shown on this thread. None or the tourist operators saw a thing until people arrived to have a look. The thing a lot of people are missing is the real time involved with people being able to do this and have it complete and ready for observation from the air in half an hour. God! It'd take me at least three hours to set up!
The first thing researchers look for in a crop circle is access by foot. The second thing they look for is a hole in the middle of the circle and the third is the bend points of the grasses to check how they happened.
Good researchers who investigate crop circles, UFO contact/abductions, spiritual infestations etc., do so from the viewpoint of confirming all possible human intervention before even looking at the possibility of extra terrestrial or extra dimensional intervention. Unfortunately, most die hard dubunkers will first discard any serious investigations and paint all phenomena with "Crack pot"paint.

<<What was the original equation?>>

zn+1 = (2zn3 - c + 1)/(3zn2 - c) ... when z3 - 1 = 0 ... ?

<<<A circle is not a circle without a center>>

true .. according to >>> (x - h)2 + (y - k)2 = r2

if r =0 then there is no circle ...

when we define r (radius) to be a line segment that joins
the center of a circle with any point on its circumference ; )