The Looping Theorem in 2D and 3D Turtle Geometry

Year: 2023 Authors: Tom Verhoeff

Core claim

For repeated turtle programs, closed and proper behavior can be characterized by total turning in 2D and screw-motion structure in 3D.

Topics

turtle geometry, looping theorems, rotational symmetry, screw motions

Domains

geometry, group-like transformations, quaternions, geometric algebra, mathematical art, generative patterning, symmetry design

Methods

theorem generalization, case analysis, screw decomposition, quaternion multiplication

Media

virtual turtle programs, 2D paths, 3D paths, supplementary illustrations

Source status

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