One of the definitions of mathematics is that it is "a science of patterns and themes". Within the scope of this definition, the current software technology facilitates the creation of visuals and patterns. Thus, GeoGebra software was used. The study was carried out in two stages. In the first stage, the Dynamic Geometry Software and the Discovery of Mathematical Concepts class was taught. In the last stage, the preservice primary mathematics teachers were given an assignment and asked to continue in groups. The groups were told that they were expected to produce aesthetically pleasing visuals and patterns. Therefore this research aimed at investigating how preservice teachers determine the design process and how they solve problems encountered during the process. Thus, as can be seen in the literature, the method and design as a long term study are the new contributions to the literature. Case study was carried out with 39 second-year preservice mathematics teachers. The research data were collected through preservice teachers' finalized projects which included a Microsoft-Word document that described in detail the process, screenshots, and GeoGebra applications. The data were analyzed by using the content analysis technique. As a result of this study, preservice mathematics teachers entered into research and analysis activities, investigated to create original designs, spent more time on the significance of visuals and patterns and so many groups made various creative tasks.