Barnsley's fern is a fractal formed by transforming a point, which is initialized to (0,0), by selecting one of four functions according to a finely-tuned probability schema. The fractal pictured below represents over 100,000 iterations of this process.

Credit to @gilesmcmullen (Python Programmer) on Youtube for formatting and coding.

                        
    import numpy as np
    import matplotlib.pyplot as plt
    import matplotlib.cm as cm

    def fn1(x,y):
        return (0.0*x, 0.16*y)
    def fn2(x,y):
        return (0.85*x + 0.04*y, -0.04*x + 0.85*y + 1.6)
    def fn3(x,y):
        return (0.2*x - 0.26*y, 0.23*x + 0.22*y + 1.6)
    def fn4(x,y):
        return (-0.15*x + 0.28*y, 0.26*x + 0.24*y + 0.44)
    fns = [fn1, fn2, fn3, fn4]

    points = 100000
    width, height = 500,500
    fern_image = np.zeros((width, height))
    x, y = 0, 0

    for i in range(points):
        function = np.random.choice(fns, p=[0.01, 0.85, 0.07, 0.07])
        x, y = function(x,y)
        ix, iy = int(width / 2 + x * width / 7), int(y * height / 12)
        fern_image[iy,ix] = 1

    plt.imshow(fern_image[::-1,:], cmap=cm.Greens)
    plt.show()