Artistic view of the prime numbers [Vue artistique des nombres premiers].
5----4----3 | | . | | . 6 1----2 . | | | | 7----8----9----10
d(N) = number of divisors of N, thus d(N) = 2 if N is a prime number (including N=1 for the sake of simplicity, when N=1 is not a prime number),and:
f(x) = an arbitrary function, for example, f(x) = xThus a first interesting picture P1 is obtained with many linear structures made of points of the same color. For example, when chosing:
f(2) = whiteand:
f(d) = black \-/ d#2the picture displays all the prime numbers till the number of points of the picture (in this case 512x512 = 262144). Then, it is known as the Ulam spiral.
1 z --> --- zthe picture plane being the Complex Plane.