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.
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.