ulam_spiral

ulam_spiral, a MATLAB code which displays the integers as a spiral of grid cells, with the primes highlighted, so show that they tend to fall along diagonals, as discovered by Stanislaw Ulam.

Licensing:

The information on this web page is distributed under the MIT license.

Languages:

ulam_spiral is available in a MATLAB version and an Octave version and a Python version.

Related Data and Programs:

ulam_spiral_test

matlab_plots, a MATLAB code which uses plotting to illustrate a mathematical structure, such as an iterative map, a fractal, a curve or surface.

Reference:

1. Martin Gardner,
   Mathematical Games: The Remarkable Lore of the Prime Number,
   Scientific American,
   Volume 210, March 1964, pages 120-128.
2. Martin Gardner,
   Sixth Book of Mathematical Diversion from Scientific American,
   ISBN13: 978-0-226-28250-3,
   University of Chicago Press, 1971.
3. Christian Hill,
   The Ulam Spiral,
   https://scipython.com/blog/the-ulam-spiral/
4. Cleve Moler,
   primespiral.m,
   Numerical Computing with MATLAB,
   SIAM, 2004,
   ISBN13: 978-0-898716-60-3,
   LC: QA297.M625,
   ebook: https://www.mathworks.com/moler/chapters.html

Source Code:

• spiral_array.m, returns a 2t+1 x 2t+1 array of integers in a spiral.
• prime_spiral.m, returns a 2t+1 x 2t+1 array in which prime integers are represented by a value of 1.