While I did make this, I can’t really take too much credit. The above image was generated using a freeware program called Paint.NET (freeware). It has both Mandelbrot and Julia Set generators, and really- stunning, right?
The Mandelbrot Set (according Wikipedia):
In mathematics the Mandelbrot set, named after Benoît Mandelbrot, is a set of points in the complex plane, the boundary of which forms a fractal. Mathematically the Mandelbrot set can be defined as the set of complex values of c for which the orbit of 0 under iteration of the complex quadratic polynomial zn+1 = zn2 + c remains bounded. That is, a complex number, c, is in the Mandelbrot set if, when starting with z0 = 0 and applying the iteration repeatedly, the absolute value of zn never exceeds a certain number (that number depends on c) however large n gets.
While admittedly, I’m completely lost in the definition above- they are a series of fractals that no matter how much you zoom down- they look the same. These fractals are all around us, and in everything (leaves, flowers, etc). They comprise life. The Mandelbrot set shows these as you zoom in.
Not to mention that they are completely stunning.
When you are looking at the actual set this is the ‘starting image’:
As you zoom in, the image is still the same, although you are looking at one small area of a much larger image. It’s fascinating.
It’s all based in mathematics. Considering that most of us aren’t capable of picturing what complex formulas would look like in a ‘more visual’ form, it is rather helpful, the images help the public at large appreciate it easily. .
You can see more from the same wiki page’s gallery: Wiki Fractal Gallery. These things really go to show that beauty is all around us, we just have to pay attention to it.