Let’s enjoy the mandlebrot first: 



Even 2000 times magnification of the Mandelbrot set uncovers fine detail resembling the full set.
If you are interested some history and information:The mathematics behind fractals began to take shape in the 17th century when mathematician and philosopher Gottfried Leibnizconsidered recursive self-similarity.
It was not until 1872 that a function appeared whose graph would today be considered fractal.
Iterated functions in the complex plane were investigated in the late 19th and early 20th centuries by Henri Poincaré, Felix Klein, Pierre Fatou and Gaston Julia. Without the aid of modern computer graphics, however, they lacked the means to visualize the beauty of many of the objects that they had discovered.
In the 1960s, Benoît Mandelbrot started investigating self-similarity, in 1975 Mandelbrot coined the word "fractal" to denote an object whose Hausdorff–Besicovitch dimension is greater than its topological dimension. He illustrated this mathematical definition with striking computer-constructed visualizations. These images captured the popular imagination; many of them were based on recursion, leading to the popular meaning of the term "fractal".