ABSTRACT
This chapter renders various examples describing how particular patterns (sequences) ensue from the assorted geometrical arrangements that repeat at the same scale, replicate at different scales (fractals) and alternating patterns of geometrical systems. It examines the occurrence of patterns in piecewise functions. Analogous to different examples, the chapter examines different patterns that originate from contrasting piecewise functions. It examines more thorough examples of piecewise functions that portray replicated patterns at the same scale as combinations of horizontal lines and diagonal lines. The chapter focuses on the geometrical examples that render the repetition of patterns at the same scale, and also focuses on a system of diminishing equilateral triangles whose dimensions and areas are resembled by a geometric sequence. It portrays an alternating system of diminishing squares and circles and expresses the lengths, radii and the areas as a piecewise sequence.
