Let the Numbers Do the Walking: Generating Turtle Dances on the Plane from Integer Sequences

Year: 2017 Authors: Adam Colestock

Core claim

The turn sequence f(n)=n mod A - n mod B can produce closed, symmetric turtle paths whose retracing behavior and symmetry order depend on A and B.

Topics

turtle geometry, modular arithmetic, integer sequences, plane symmetry

Domains

discrete mathematics, modular arithmetic, symmetry, turtle art, generative design, mathematical art, visual pattern design

Methods

discrete parametric function, turtle graphics algorithm, sequence-based turn control, continuous-function sampling

Media

LOGO, Scratch, Processing, turtle geometry

Source status

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