A fractal is a self-similar pattern that is observable at any scale.
The Barnsley Fern is a fractal image concept created by Michael Barnsley that achieves the fractal status through replicating a point in four matrices with the appliance of slight shiftings through a large number of iterations.
The koch snowflake is a fractal image concept created by the mathematician Helge von Koch. It achieves the fractal status through creating an equilateral triangle, then dividing its lines into four equally-sized lines forming a spike - iteratively.
The Pythagoras Tree is a fractal image concept created by the mathematician Albert E. Bosman and named after the ancient greek mathematician Pytagoras. It achieves the fractal status through having a vertical straight line that splits to two diagonal lines, which in turn split by two lines each, for a certain number of iterations.