ABSTRACT
This chapter begins with examples of nature’s patterns, and portrays the repetitive alpine patterns of the Rocky Mountains in Rocky Mountain National Park. It provides several geometry examples and provide varieties of examples that characterize decomposition of figures at the same scale and geometrical fractals that resemble decomposition of figures at diminishing scales. Piecewise functions have numerous applications in describing economic cycles, population dynamics, weather patterns, signal processing, neural networking and other natural phenomena. The chapter examines assorted examples of piecewise functions that guide us to various recognition of patterns. The Fibonacci Sequence emerges in nature’s numerous patterns such as the structure of pine cones, trees, leaves, sunflowers, seashells, waves, storm systems and the galaxies’ formations. The chapter provides an analysis of piecewise or alternating patterns (sequences) that consist of two or more fragments and that render periodic behavior and patterns.
