In this page we shall collect the data and images related to our interest in the geometrical
properties of the contiguos line segments formed by the primes in the Ulam square.
Leszek J Chmielewski and Arkadiusz Or這wski Authors
Copyright
Copyright (C) Leszek J Chmielewski and Arkadiusz Or這wski.
Each of the sets in the table below for the Ulam square of the specified size contains:
Text files:
file with information on the size of the square, numbers of primes, maximum prime;
files with listings of segments of length from 4 to 16 pixels (empty files if there are no segments with a length).
Images:
Ulam spiral;
images with visualizations of segments of length from 4 to 16 pixels (those with nonzero number of segments); for some larger squares the images can be unavailable.
L. J. Chmielewski, M. Janowicz, G. Gawdzik and A. Or這wski.
Contiguous line segments in the Ulam spiral: Experiments with larger numbers.
In Artificial Intelligence and Soft Computing: Proc. Int. Conf. ICAISC 2017,
pages 463-472, Zakopane, Poland, 11-15 Apr 2017.
LNAI series Vol. 10245, Springer.
(doi:10.1007/978-3-319-59063-9_41)
(PDF)
L. J. Chmielewski, A. Or這wski, and G. Gawdzik.
Segment counting versus prime counting in the Ulam square.
In Proc. 9th Asian Conference on Intelligent Information and Database Systems ACIIDS 2017, Part II,
pages 227-236, Kanazawa, Japan, 3-5 Apr 2017.
LNAI series Vol. 10192, Springer.
(doi:10.1007/978-3-319-54430-4_22)
(PDF)
L.J. Chmielewski, A. Or這wski and M. Janowicz.
A study on directionality in the Ulam square with the use of the Hough Transform.
In Hard and Soft Computing for Artificial Intelligence, Multimedia and Security: Proc. Conf. ACS 2016,
pages 81-90, Mi璠zyzdroje, Poland, Oct 19-21, 2016.
Advances in Intelligent Systems and Computing series
Vol. 534, Springer, 2016.
(doi:10.1007/978-3-319-48429-7_8)
(PDF)
L.J. Chmielewski, A. Or這wski.
Finding line segments in the Ulam square with the Hough transform.
In Computer Vision and Graphics: Proc. Int. Conf. Computer Vision and Graphics ICCVG 2016,
pages 617-626, Warsaw, Poland, Sept 19-21, 2016.
LNCS series Vol. 9972, Springer.
(doi:10.1007/978-3-319-46418-3_55)
(PDF)
L.J. Chmielewski, A. Or這wski.
Hough transform for lines with slope defined by a pair of co-primes.
Machine Graphics & Vision, 22(1-4):17-25, 2013
[open access].