Programming the Sierpiński Carpet fractal using Java involves creating a 3-by-3 grid of squares with recursive methods.A recursive method is utilized to achieve the infinite effect of fractals by calling itself.Key steps involve setting up variables for width and height, creating a JFrame, defining a FractalShape class, and implementing recursive methods.The recursive method CreateFractal initiates the process, while FractalRecursive handles the generation of the fractal patterns in a nested loop.