Fractals are seen in many areas of nature, such as geographical terrain.  It is fairly easy for a computer-generated fractals to look identical to real life terrains.  This is an algorithm to create it.

First, start with a line with two endpoints:
 

Now find the midpoint of this line, and displace that point upwards or downwards by a random amount in a fixed range, called H.  Then we may find something like this:

Now we have two line segments.  Recursively run the same algorithm on each line segment.  We may get something like this:

And so on and so on.  Thus, this algorithm for 8 iterations, for four different lines may produce:

Here are four possible terrains.  However, they look very different.  This is because I left out the most crucial step of the algorithm, which is for each iteration, we reduce H.  This means that in each iteration, we reduce the range of the iteration.  Varying the amount of reduction will result in different terrains, such as above.  The chart for the colors are:
 

Thus, we see that the higher the value for H, the less jagged than with a lower value of H.  The value that the range is calculated is by taking a random number between 0.0 and 1.0, and then multiplying it by H * 2^(-H).  Thus, if you have a H with the value of 1.0, then your displacement range will be halved each time.  Having a low H value means your range will not be reduced, and the terrain will be jaggy.

Here are three more examples of the four lines at eight iterations:

Here are four examples of four lines at sixteen iterations.  Notice how the more iterations, the more jagged the picture is: