Search results
May 27, 2017 · The Ulam spiral containing prime numbers up to slightly above \ (10^9\) was investigated from the point of view of the existence of contiguous straight line segments. This paper was a continuation of the previous works in which the Ulam square of size up to \ (5001 \times 5001\) were analyzed, for directions expressible by quotients ...
Feb 26, 2017 · In we have analyzed the directional properties of the segments in the Ulam spiral. The accumulated results make it possible to look for other regularities in the set of segments present in the Ulam spiral. Assume the square is \(S\times {}S\), so it contains \(P=\pi (S^2)\) primes.
In random images the densities of the longer segments and the lengths of the longest ones are considerably smaller than those in the Ulam square, while for the shorter segments it is the opposite.
Sep 10, 2016 · A version of the Hough transform designed specially for detecting sequences of pixels forming segments of straight lines with the slope defined by an irreducible fraction was used to find line segments in the Ulam spiral.
May 27, 2017 · In our previous papers we have investigated the directional structure and the numbers of straight line segments in the Ulam spiral.
Download scientific diagram | Number of segments versus length of the segment for various sizes of the Ulam square, for direction array N = 10. If the number of lines is zero the data point...
Contiguous Line Segments in the Ulam Spiral. . . 471 Fig. 7. The Ulam square of size 2001×2001 for direction array N = 50 with the new segments of length 13 in blue ( ), green ( ), red ( ) and magenta ( ). The segment present already for N = 10 shown in yellow ( ). Grey pixels ( ): primes, black pixels: other numbers.
