11481

Generalized Ulam Sets in the Plane

This Demonstration plots a list of points of the generalized Ulam set in the plane after steps of iteration. The recursive rule to generate is to append vectors to the previous set of minimal Euclidean norms that can be uniquely written as the sum of two distinct vectors from . The specified list of linearly independent initial vectors completely determines the points.
Set the "step size " for the plot, keeping in mind that any setting may be slow.
The list of two or more initial vectors may be specified by selecting one of the preset initial vector combinations or randomly.

SNAPSHOTS

  • [Snapshot]
  • [Snapshot]
  • [Snapshot]

DETAILS

References
[1] N. Kravitz and S. Steinerberger, "Ulam Sequences and Ulam Sets." arxiv.org/abs/1705.01883.
[2] M. D. Schmidt, "Pair Correlation and Gap Distributions for Substitution Tilings and Generalized Ulam Sets in the Plane." arxiv.org/abs/1707.05509.
[3] M. D. Schmidt. "Ulam-sets." (Jul 31, 2017) github.com/maxieds/Ulam-sets.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.









 
RELATED RESOURCES
Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-Step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2017 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+