Square Koch Fractal Curves

The classic Koch fractal curve is recursively created by starting with a line segment and then recursively adding a triangular bend in the center of each segment. Variations can be created by using a square shape instead of a triangle in the replacement rule. The type 1 curve is a direct analogy to the classic Koch curve, replacing each line segment with five smaller segments placed at right angles. The type 2 quadratic curve—also known as the 3/2 curve and the eight-segment Koch curve—uses a similar motif that replaces each segment with eight smaller segments.