Designing Koch-Like Curves
Vincent J. Matsko · College Mathematics Journal · 2017
SummaryWhen the angles are changed in the usual algorithm to generate the Koch snowflake, a wide variety of images can be produced, some of which possess rotational symmetry. Using elementary number theory, we parameterize infinitely many such images and determine many geometrical properties of families of images, such as which orders of symmetry are possible and exactly how many sets of parameters produce an image with a given complexity and symmetry.