There exists a general consensus in aesthetics that beauty lies at the intersection of order and disorder. The perfect order is tedious and therefore not attractive. The chaos is incomprehensible to our brain and therefore is equally unappetizing. When we depart from order without resulting in complete chaos, maintaining an unstable balance between regularity and mess, often we get a result that surprises and thrills, so that we may define it beautiful.
Prime numbers are the perfect incarnation of this idea of aesthetic and hence are a luscious ingredient of beauty and art. Prime numbers are infinite in number and as they grow they become rarer and rarer. However, mathematicians conjecture there are infinitely many close pairs of primes (like twin primes, that distance 2, or cousin primes, that distance 4). The exact distribution of primes within the natural numbers is still a mystery and is related to one of the most famous unsolved questions in mathematics, dating from 1859: the Riemann hypothesis, one of the Millennium Price Problems.
We propose an artistic visualization of primes, called Primenuum. The idea behind it is quite simple and came to the beautiful mind of artist Sergio Scalet from Hackatao while thinking at the branching process of natural trees. The idea was then coded in Processing by me:
Scan the natural numbers starting from 1. For every number, draw a small segment of fixed size, starting from the center of the canvas and moving from left to right. When a prime number is encountered, turn the drawing direction 90 degrees clockwise (alternatively, turn the canvas 90 degrees counter-clockwise).