Math
Everything has started from genius matematicians like Mandelbrot, Julia or Sierpinski. They showed other ways of defining nature through math.
Everyone can create fractals but very few can see beyond iterations to get a picture that is worth the greatest works of art.
Just to mention, I am not Rembrandt of iterations or Monet of zoom. This is one of my passions and if you find some pleasure from my works then I am more than just happy.
Mostly, fractals are pleasant to watch, enjoyable, they feed imagination and leave a lot of space for your expression. This is the reason I got into them.
I tested several fractal-generating apps and have a few I like the most. As my best buddies I can mention Mandelbulber 3D, Apophysis and Sterling2. With these three apps I did most of my works and they give me a lot of fun when zooming and iterating.
Everything has started from genius matematicians like Mandelbrot, Julia or Sierpinski. They showed other ways of defining nature through math.
They do the magic. More iteration you will set, more calculations your machine will perform and more complex picture you will get.
Tons of colors make the fractals so pleasant. Playing with color variations of the same element can totally change the outcome.
No matter how far you will get with the fractal, you will always find it decent. Zooming is addictive, especially in apps like XaoS.
Besides programs mentioned above I can also recommend Incendia, Ultra Fractals, Chaotica, XaoS, Tierazon (project website is from 1998).
They are specific, non linear class of fractals. They come in more abstract, irregular forms.