Wolfram Library Archive


All Collections Articles Books Conference Proceedings
Courseware Demos MathSource Technical Notes
Title Downloads

Complex Continued Fractions
Author

Doug Hensley
Revision date

2005-07-21
Description

Schmidt Circles The Asmus Schmidt algorithm effectively partitions the plane into regions, then subregions, and so on, and in this way, each point is encoded by the sequence of regions to which it belongs. Since it cuts it infinitely fine in the end, visualizing the partition requires some compromises.
It is by this method that Complex Continued Fractions are calculated. Seven matrices are used.
  • v1={{1,I},{0,1}}
  • v2={{1,0},{-I,1}}
  • v3={{1-I,I},{-I,1+I}}
  • e1={{1,0},{1-I,I}}
  • e2={{1,-1+I},{0,I}}
  • e3={{I,0},{0,1}}
  • c={{1,-1+I},{1-I,I}}
Each use of these matrices divides the plane into seven parts. Mathematica is well-suited for studying successive generations. A PDF and EPS of many generations is shown.
Subjects

*Mathematics > Calculus and Analysis > Complex Analysis
*Wolfram Technology > Programming > 3D Graphics
URL

http://www.maa.org/editorial/mathgames/mathgames_03_15_04.html
Downloads Download Wolfram CDF Player

Download
schmidtcircles.pdf (403.9 KB) - PDF Document
Download
schmidtcircles.eps (199 KB) - Enhanced postscript file
Download
schmidtcircles.nb (261.5 KB) - Mathematica Notebook