GSG is an end-user-programmable archiving and interface system that the designer may use and is capable of manipulating codes to generate recursive shapes. GSG generates a wide variety of shapes and patterns. Simple or complex algorithmic formulas and/or transformation rules may be utilized to alter, modify, replicate, or transform the current geometric shapes or patterns. There are endless numbers of design styles, which are created by limited sets of rules. GSG is a design tool that allows the designer to choose and apply individual rules and algorithm to generate geometric shapes or patterns. Additionally, depending on how the formulas and order of transformation is applied, we may also alter, modify, replicate, or transform the current chaos theory based shapes or patterns.