Ulam Spiral

As a mathematical mainframe to design the volumetric base of Instants of Metamorphosis v.01, we have the Ulam Spiral. The installation will be presented at the ABCIBER 2011 conference and exhibition next November in Florianopolis, Brazil:



an article:
Observations on the Regularity of Prime Number Distribution
by Peter Marteinson
http://french.chass.utoronto.ca/as-sa/ASSA-No14/article7en.html

Abstract:
Stanislaw Ulam’s (1964: 516) most general observation on his famous spiral, that a “property of the visual brain” allows patterns relating to the characteristics of primes to be discovered, may indeed stimulate the mathematical imagination, and inspire further creative attempts at visual pattern recognition in this area, but his spiral (fig.1), like its derivatives, has yet to be successfully interpreted in terms of possible arithmetic principles that can explain the genesis of the known distribution of prime numbers. Of his spiral he says only that it “appears to exhibit a strongly nonrandom appearance” (Stein et al. 1964). A corollary of this somewhat disappointing observation is that Euler’s pessimistic prognosis has yet to be disproved: “Mathematicians have tried in vain to this day to discover some order in the sequence of prime numbers, and we have reason to believe that it is a mystery into which the mind will never penetrate” (cited by Ivars Peterson in Science News, 5/4/2002). The Encyclopædia Britannica (2004) continues to suggest this consensus is alive and well, referring in an article entitled “Elementary Number Theory” to “the irregularity in the distribution of primes” which “suggests that there is no simple formula for producing all the primes.”






other connections:

On Quantum hall effect:
http://eskesthai.blogspot.com/2006/09/quantum-hall-effect.html

wiki: Ulam Spiral:

http://en.wikipedia.org/wiki/Ulam_spiral


The distribution of prime numbers on the square root spiral
by Harry K. Hahn, Robert Sachs
http://arxiv.org/abs/0801.1441