👉 To demonstrate the beauty of mathematics, consider the concept of fractals, which are geometric shapes that exhibit self-similarity at different scales. The Mandelbrot set, a famous fractal, is generated using a simple iterative formula: \( z_{n+1} = z_n^2 + c \), where \( z \) and \( c \) are complex numbers. By plotting the values of \( c \) that keep the sequence bounded, we create a visually stunning boundary with intricate patterns repeating infinitely. This example showcases how a deceptively simple rule can produce complex, infinitely detailed structures, reflecting the deep interconnectedness and infinite complexity inherent in mathematical systems.
