* Sierpinski triangle is an example of NonEuclidean shape. 
* All man made objects belong to Euclidean geometry consisting of
lines, planes, rectangular volumes, arcs, cylinders, spheres etc. Their
dimensions are integral in nature i.e. 1,2,3 etc or 4 (including time) 
* Increase in size S is given by the formula
S= L^{D }
where
L is linear scaling & D is dimension or D = log (S) / log (L) ; 
* In case of Euclidean objects lying in a plane, when linear scaling
is doubled, size increase 2^{2} =4 times since D=2 and if in
space,
linear scaling is doubled, size increase 2^{3} = 8 times since D=3 
* However, in case of NonEuclidean shaped objects lying in a plane,
if they are linearly scaled by a factor L ( for example 2 ), the area or
size does not increase by L^{2} i.e. 2^{2} =4 times but
by an nonintegral amount of D 
* These types of geometries are called fractals and the physical and
biological universe abounds with fractal shapes. 
* Two identifying features of Fractal shapes : (1) They look similar
to each other (selfsimilarity) but are not exactly same. Exa Any two
Human beings. (2) Their dimension is not integral, i.e. 2.45 or 3.973
etc. in stead of exactly 2 or 3. 
* The whole universe is a fractal and each fractal is an universe
unto itself since it is infinite. 
* Whereas Euclidean objects are described by a simple algebraic
formula, there is no such formula for fractals. These are described by
iterative or recursive alogarithm. 
*
Wacław
Sierpinski was a Polish mathematician (18821969) Who constructed
the triangle which is a fractal image. Take an equilateral triangle.
Join the midpoints of 3 sides to form a triangle. Remove the inner
triangle and Continue joining the mid points of the generated 3
triangles. Again remove the middle triangle and continue with a
particular no. of iterations. 
