Next Generation of Star Patterns

TL;DR

This paper introduces two innovative parametric methods for generating complex star patterns and filling gaps in tile operations, enabling the creation of infinite new patterns with adjustable parameters.

Contribution

The paper presents a novel concentric circle-based parametric approach and a tangent circle-based tiling method for generating diverse star patterns.

Findings

Generated a wide variety of star patterns with adjustable parameters

Demonstrated the use of tangent circles for efficient tiling and gap filling

Developed Android apps to implement the proposed methods

Abstract

In this paper we present two new ideas for generating star patterns and filling the gaps during the tile operation. Firstly, we introduce a novel parametric method based on concentric circles for generating stars and rosettes. Using proposed method, completely different stars and rosettes and a set of new and complex star patterns convert to each other only by changing nine parameters. Secondly, we demonstrate how three equal tangent circles can be used as a base for generating tile elements. For this reason a surrounded circle is created among tangent circles, which represents the gaps in hexagonal packing. Afterwards, we use our first idea for filling the tangent circles and surrounded circle. This parametric approach can be used for generating infinite new star patterns, which some of them will be presented in result section.Two Android apps of proposed method called Starking and Tilerking are available in Google app store.