Solutions to a Functional Equation via Stern-Brocot Tree Fractions

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

This Demonstration generates solutions of the functional equation starting from . The solutions correspond to Stern–Brocot tree fractions at level . Change at the top for more complicated solutions. Click the " versus " button to see a plot of the computed solution depending on as a parameter, which you can vary with the "vary or " slider. Similarly, click the " versus " button and vary the parameter . Finally, click the "singularities" button to see the points where the computed function is not defined. The color-coding of those points helps identify where the parts of the solution originated.

[more]

Mouse over the plot to see the values or equations of the data. The black and red circled points are related to Stern–Brocot tree fractions. The absolute values of the components of the black circled points are the values of all Stern–Brocot tree fractions up to level . The red circled points have a component with an absolute value equal to the Stern–Brocot tree fractions at level .

[less]

Contributed by: Jan Fiala (November 2016)
(UVa Wise)
Open content licensed under CC BY-NC-SA


Snapshots


Details

Reference

[1] J. Fiala, "Statistical Mechanics of Farey Fraction Spin Chain Models," Ph.D. thesis, Department of Physics, The University of Maine, 2004. www.library.umaine.edu/theses/pdf/FialaJ2004.pdf.



Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.
Send