The reason why your image isn''t a fractal is because it doesn''t involve an actual methematical process. Although in a way it is, as you are applying a "simple" process to an astute mapping repetitively. It''s like er... forgot his name. Some guy''s horse-shoe folding. In any event, the main problem is that you can''t zoom in infinitely. You create noise and apply a process to it an infinit amount of time. It''s like creating a random noise mapping and applying a smoothening filter to it. Although the process is fractal, when you zoom in your noise "particles" will become more and more distant and applying the process won''t give you a constant level of detail anymore.
The line->triangle thing you described is, indeed, a well-known fractal called the Koch curve. There''s a variation called the Koch snowflake that involves applying that to a triangle. Pretty dang nice.
