Sierpiskiháló

Sierpiskiháló, also known as the Sierpinski carpet or Sierpinski sieve, is a fractal geometric shape named after the Polish mathematician Wacław Sierpiński. It is constructed by iteratively removing the central square from each square in a grid, then repeating the process on the remaining squares. The result is a pattern of squares that becomes increasingly complex and intricate as the number of iterations increases.

The Sierpinski carpet is a two-dimensional analog of the Cantor set, another famous fractal. It has a Hausdorff dimension of approximately 1.893, which is greater than its topological dimension of 2. This property makes it a type of fractal known as a space-filling curve, as it can fill a two-dimensional space while having a non-integer dimension.

The Sierpinski carpet has several interesting mathematical properties. It is self-similar, meaning that it can be divided into smaller copies of itself. It is also connected, meaning that there is a path between any two points in the carpet. Additionally, it has a finite area but an infinite perimeter, which is a characteristic property of fractals.

The Sierpinski carpet has applications in various fields, including computer graphics, where it is used to generate complex textures and patterns. It is also used in the study of fractals and their properties, as well as in the design of algorithms for generating and analyzing fractal shapes.