Many important spatial patterns of Nature are either irregular or fragmented and it is impossible to describe their form by classical geometry. For example,the coastline of a typical oceanic island is neither straight , nor circular , nor elliptic , etc.
Therefore in many cases it is impossible to remedy this absence of geometric representation by using a family of shapes called "fractals". Some fractal set are curves , other are surfices , still other are cloud of disconnected points.
A definition of "fractal" might be "irregular , with constant digressions and interruptions" , because the term "fractal" becomes from the Latin adjective "fractus" which means "irregular or fragmented".
This term can be applied to mathematical fractal sets and also to some natural patterns like physical Brownian motion , which is the motion agitating each small particle suspended in a fluid and is the prime example of natural fractal.
The branch of mathematics that studies form is topology; it teaches us , for example , that all triangles which have the equal measure of two angles have the same form because we can always put one inside another one.
Obviously , this particular aspect of the notion of form is not useful in the study of individual coastlines , since it simply indicates that they are topologically identical to each other. So if we want discriminate between different coastlines , topological form is a too general instrument but we can use another instrument called "fractal form". In fact coastlines of different degrees of irregularity tend to have different fractal dimensions and differences in fractal dimension express differences in non-topological but fractal aspect of form