WXH-Fibonacci Sequence and Fractal Algorithms

In this article, we explore several mathematical concepts and their computational implementations: the WXH-Fibonacci sequence, Koch curve algorithm, dynamic Von Koch fractal curves, midpoint displacement method for generating Sierpinski carpets, and fractal butterfly patterns. The Fibonacci sequence represents a fascinating numerical series where each number equals the sum of the two preceding numbers, typically implemented using recursive functions or iterative loops in programming. The Koch curve constitutes a classic fractal pattern constructed through recursive subdivision of line segments into triangular protrusions. The dynamic Von Koch fractal variant introduces animation capabilities by progressively modifying iteration parameters. The midpoint displacement method for Sierpinski carpet generation employs recursive geometric partitioning, where squares are repeatedly divided into nine smaller squares with the center removed. Finally, the fractal butterfly demonstrates a beautiful and complex pattern emerging from iterative transformations of geometric shapes, often implemented using affine transformations in computational geometry. Through this technical exploration, readers will gain deeper insights into these sophisticated mathematical concepts and their programming implementations.