The reason fractals are involved is because a fractical is indeed a dynamical system with initial condition sensitivity. Take the Koch Snowflake:
Koch snowflake - Wikipedia, the free encyclopedia
This is generated using an iteration of a general rule. Think of it as a programme which does this process any time it sees a straight line. The process is this:
Whenever we come across a straight line segment:
1. divide the line segment into three segments of equal length.
2. draw an equilateral triangle that has the middle segment from step 1 as its base and points outward.
3. remove the line segment that is the base of the triangle from step 2.
The Koch Snowflake is what you get when you apply these iterations again and again to a shape that initially started off as an equilateral triangle. However, if our initial shape wasn't initially an equilateral triangle, then only 1 iteration would lead us to diverge from the koch snowflake, and the more iterations, the more we would diverge! So we can clearly see that the result of fractals is very sensitive to the initial conditions. Try it yourself. Take random shapes made of straight lines (they need not be equal in length!), and iterate the above process ^. You will see how it diverges from the Koch Snowflake.