Many crop formations carry real mathematics. Some encode numbers. Some draw fractals that need a computer to plot. These are the clearest examples in the Crop Signals catalogue.
Fractals
A fractal is a shape that repeats itself at every scale. Several of the highest rated signals are fractals.
- Mandelbrot set (Kidlington, Oxfordshire, 1992). The best known fractal in mathematics, drawn in a field.
- Stonehenge Julia set (Wiltshire, 1996). A Julia set spiral that appeared in a field opposite Stonehenge.
- Trinary Julia set (Windmill Hill, Wiltshire, 1996). Three Julia set arms around one centre.
- Sierpinski triangles (Chilbolton, Hampshire, 1999). A triangle fractal outlined in small circles, two years before the Arecibo response appeared in the same field.
- Milk Hill galaxy spiral (Wiltshire, 2001). Six spiral arms made from more than 400 circles.
Numbers and constants
- Pi (Barbury Castle, Wiltshire, 2008). The first ten digits of pi encoded in a notched spiral.
- Kozárovce notched life seed (Slovakia, 2009). Notched rings in the same style as the pi formation.
- Euler’s identity disc (Wilton Windmill, Wiltshire, 2010). A binary disc that reads as Euler’s identity, ei¤Ç + 1 = 0.
Sound
Cymatics is the study of the shapes sound makes in sand or water on a vibrating plate. Many formations look like these shapes. The post on cymatic patterns goes into more detail.
DNA
- Infinite binary DNA disc (Crooked Soley, Berkshire, 2002). A DNA spiral in six sections drawn as binary bits on a disc.
- Boryeong DNA agrogram (South Korea, 2008). A second DNA design, this time far from Wiltshire.
Star maps and replies
- Arecibo response (Chilbolton, Hampshire, 2001). A reply to the radio message sent from Arecibo in 1974, with key details changed.
- Origin star map (Roundway Hill, Wiltshire, 2014). A pattern that looks like a star map, perhaps of the senders’ home star.
What it adds up to
Any one of these could be the work of a skilled team with a plan. Taken together, the range of mathematics is hard to put down to pranks alone. Every formation in the catalogue has a rating, so you can judge each one for yourself.
