Quaternion Julia Set

The classical filled-in Julia set contains points in the complex plane that remain bounded on repeated application of quadratic function = . Quaternions are 4-tuples of real numbers with a noncommutative multiplication; this Demonstration extends the idea to show a three-dimensional section of the four-dimensional Julia set.



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


The Demonstration renders a number of cases, selectable from the top popup menu, some in quaternion space and others that relate to classical Julia set forms in degenerate complex space. Each case is distinguished by the quaternion constant, c, and the definition of the section plane The section of the model settings permits setting the threshold against which the norm of the recursion result is compared. The image settings include the image sampling points and whether axes should appear. Selecting the "high resolution" button enables setting the maximum number of recursions, setting the intercept of the section plane, and selecting a full image or only a quadrant. In addition, the advanced setting extends the menu ranges from which the threshold and the number of image sample points can be selected. Some of these settings will produce long computing times.
    • 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.

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 © 2016 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+