Tree Branching in 4D

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.

In 4D, multiplication by quaternions gives a linear transformation, which ensures that the branches have the same lengths relative to their trunk, and the same angles, regardless of the orientation of their trunk. The same thing happens in 2D with complex multiplication, but in 3D such a transformation is not possible, which is not unrelated to the forced vanishing of vector fields on the sphere. In this Demonstration, the fourth dimension, serving as a hidden variable, is used to color the edges for even more visual interest. The hidden fourth dimension plays a key role in maintaining the symmetry of the branchings, unlike its 3D counterpart. One can think of the Demonstration as occurring in 4D and imagine that the variable theta determines the angle the branches take from their parent branch.

Contributed by: Todd Rowland (March 2011)
Open content licensed under CC BY-NC-SA


Snapshots


Details

detailSectionParagraph


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