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SELF-SIMILARITY



        Draw a triangle.  Within that, draw  another inverted triangle.  Now we get 3 triangles in 3 corners.  Within these triangles, again draw inverted triangles.  Now repeat the procedure as many times as possible.  The emerging figure is called the sierpinski gasket.  This is the good example for self similarity.  The overall structure is replicated many times throughout the figure.  And it is even present at the microscopic level.

      To put in nutshell; using self similarity technique and repeating infinite number of times, one can generate complex figures.

      These figures does not fall in a straight line(one dimension) or occupy the entire area of the square (two dimension).  They fall somewhere in between dimension 1 and 2.  So they are said to be having fractional dimension.  Hence they are called FRACTALS.  Fractals occurs everywhere in nature.

 Examples: Trees, leaves, snowflakes, peacock feathers, seashells, lungs structures, lightnings, broccoli, ferns, river delta and so on.  
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