Sources of Flow as Sources of Symmetry: Divergence Patterns of Sinusoidal Vector Fields

Year: 2014 Authors: Judy Holdener; Marie Snipes

Core claim

For vector fields of the form sin(ax)cos(by) i + sin(cy)cos(dx) j, the parity structure of a,b,c,d determines vertical, horizontal, and diagonal lines of incompression.

Topics

vector fields, divergence patterns, symmetry, black-and-white pattern generation, fluid flow analogy

Domains

multivariable calculus, vector calculus, trigonometric functions, 2-adic valuation, pattern design, black-and-white art, visual symmetry, public sidewalk design

Methods

theorem and proof sketch, periodicity analysis, cosine identities, pattern visualization

Media

MAPLE plots, black and white images, vector field diagrams, photographic sidewalk example

Source status

This page publishes metadata and extracted analytical signals only. Raw PDF and full OCR text are kept local for now.