The Sierpinski triangle

The Sierpinski triangle is one of the most basic types of geometric images known as fractals.



 

The Sierpinski triangle is a deterministic fractal. It has the basic properties that are common to all fractals like recurrence : whatever part of the triangle you take, if you magnify it, you will find exactly the same triangle in it again and again.
Here is a picture of the Sierpinski triangle :
 
 

What is very interesting with the Sierpinski triangle is that you can generate it very easily in more than one way. In this report are described two different sorts of construction :


There are many other ways to generate it and sometimes it happens in surprising ways like in the modulo 2 representation of the Pascal Triangle.
The same process can be also applicated to a square, it is called the Sierpinski carpet.