"Mathematics, rightly viewed, possesses not only truth, but supreme beauty" -- Bertrand Russell

Today I had an opportunity to attend a lecture on Fractals and Chaos theory. Mathematics unraveled with all its stunning beauty. I have always felt that if I had more understanding of complex mathematics that describes the various natural phenomena I could see through the natural beauty which otherwise remains hidden.One such concept is Fractals. Here I'am trying to make a humble effort with whatever limited knowledge I have about Fractals.

In very simple terms, fractals are geometrical figures that are generated by starting with a very simple pattern that grows through the application of rules.
Here is a simple illustration starting off with a plus sign and applying it recursively.

A fractal is "a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole"- concept of self similarity. Take for example the case of seashore image taken from a satellite. The seashore is a highly irregular pattern but if we try to zoom into a particular portion, there is a similarity in that zoomed portion corresponding with the complete seashore.Another important example is the case of clouds which are highly irregular in geometry.
Many more mind boggling structures are found in nature.
Definitely this is mathematics at its best :)