Julia Set Crop Circle

The Julia Set is the world’s second-most-famous fractal. It is a pattern of never-ending complexity. As you zoom in closer at smaller and smaller scales, you see what looks like the whole pattern at a larger scale — but not quite. There are little differences, and when you zoom in on the little differences, a new variation opens up.


The Julia Set is generated very simply by starting from each point (x,y) and applying a simple arithmetic procedure over and over again. For some values, the repeated procedure gets bigger and bigger without limit. For other values, the same repeated procedure remains finite within a well-defined box forever. It is these “other values” that are defined to be the Jullia set. And the curious thing is that the map of the Julia set doesn’t demarcate some region of the (x,y) plane that you could shade; rather there are points infinitely close together where one point is in the Julia set and the other is not.

Actually, there is a family of Julia sets parametrized by a single complex number (or two real numbers).

On July 7, 1996, across the street from Stonehenge, the field was mowed or flattened in such a way as to create an impression (from the air) of the Julia set.

LiveScience https://www.livescience.com/26540-crop-circles.html

People speculate about aliens or druids having done this. If it was done by human hands, it was very labor-intensive and intricately planned. My favorite theory is that the grass is trying to send us a message that it is an intelligent superorganism.

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