# Publication: An Experimental Study On Creating Process Of Geometric Patterns

2015-12

## Abstract

Artists and designers use geometric patterns to cover surfaces since ancient times. In the 13th century the architectural works show artists have a broad knowledge of creating geometric patterns. Mathematicians conduct researches and achieve creation principles of these patterns barely in the 20th century. In this context, the principles of patterns can be known by its designer but cannot be distinguished easily with a deductive approach. Geometric shapes that are typically repeating in order form a geometric pattern. Patterns are seen as an integrated composition of geometric shapes. Nowadays, computer-based programs help to create various patterns fast and efficiently. Mathematical operations are defined to make transformations on shapes. Executing simple transformations like moving, copying, mirroring and rotating on an initial shape creates 2D geometric patterns. The first objective of this study is to search the generation process of geometric patterns and find out which parameters are used to create these patterns. This study aims not only to create shapes or geometric pattern alternatives but also to teach generation principles of geometric patterns to design students experimentally by a generative code. In the scope of this study, 2D geometric patterns are studied which are analyzed by a deductive approach. According to analysis, the following parameters are used in generation process; Specification of initial shape / Position of initial shapes / Distance between repeated shapes / Number of the repetition of x and y-axis / Determination of the angle transformations By changing these parameters experimentally in coding interface, the transformation of patterns and variety in pattern geometry are examined. Before changing parameters, the main structure of code modified three times. At the first coding, hexagon shape is created by using simple lines. By copying hexagon ten times on “x” and “y” axis and moving one shape (hexagon) many different patterns are created. Besides, sub shapes are emerged in the pattern, which are not hexagons anymore. At the second coding, changing the edge number of initial shape is transformed hexagon into a pentagon. The angles between pentagons edges are modified, and pentagons become stars with different angles. These star geometries also rotate on the axis to generate different geometric patterns. During the third modification of code, hexagons edge number is set as a variable. Changing the edge number creates a pattern that includes lines, triangles, square, pentagon, hexagon and polygons with more edges than six. As a result of modified parameters like sizes, positions, edge numbers and angles many unpredictable patterns emerge. This study shows the efficiency of coding on pattern generation. Emerged shapes can be used again as an initial shape, and new patterns can be generated with a high variety.

## Keywords

geometric pattern, parametric design, shape, sub shape, coding