INTRODUCTION TO FRACTAL GEOMETRY

- What is a fractal?
- Computers and fractals
- Fractals in nature
- The philosophy in fractals
**Fractal geometry in the Crop Circles**

## Fractal geometry in the Crop CirclesCrop Circle fractals were first introduced when the Mandelbrot fractal was printed in crop in 1991. But was it really the Mandelbrot set? No, actually it was more like a simplified portrait of it. It was called a fractal mostly because it so closely resembled the most famous fractal in the world! The real breakthrough of fractal crop circles, however, happened in the season of 1996, with formations such as the Stonehenge "Julia Set" and the Oliver's castle snowflake. The year 1997 has brought triangular fractals. As the first pictograms, the "keys", "insects", "dolphins" etc. were more like hieroglyphs or technical blue prints (not that this kind of formations have totally ceased from appearing!) the fractals are more like art or visual presentation of some universal laws... Although fractal formations might appear to be much more complex than others, in a way even a fractal with hundreds of circles or lines might be simpler than the most basic insectogram. This is the case for example with the 1997 Silbury hill Koch Snowflake. This beautiful pattern is actually just a regular triangle that is repeated within itself according to a very simple rule - as the animation demonstrates: Of course you notice that in the crop version of the fractal the two last generation triangles have been replaced with circles. Why? Perhaps we'll never know but we can speculate with different possible explanations: 1. The circle makers like to put something special in each formation; something to puzzle our minds. 2. There is a certain (not technical) reason why every crop circle must have the circular element. 3. The technique that is used to make the pictograms doesn't allow the making of very small triangles, but small circles can be made - this can be due to the "resolution" of the "canvas". 4. The formation is not meant to be a perfect fractal. It looks like it's supposed to look and fractal geometry has intentionally been used just as one element. Option number 3 was the first one that came to my mind. But any of the others - or all of them - might be true. Whether the Fractal Crop Circles will keep on increasing in number and complexity or there'll be something totally different in the future years - we'll see! |