Mathematical concepts are all around us. The Golden Ratio is derived from aesthetic measurements in the plant world. Snowflakes are actually precise symmetric structures on a molecular level. Even the man-made stock market follows a geometric figure - a fractal! The foundation to understanding patterns in the world around us lies in the study of sequences, series, and fractals. We will focus on fostering mathematical thinking through studying selected examples - mastering the underlying fundamental ideas as well as their common properties. To further engage with the material, students will learn how to use an online software to create fractals and other visual representations. The course will culminate with a final project: creating their own sequence/series/fractal.