Sierpinskikolmio

The Sierpinski triangle, also known as the Sierpinski gasket or triangle, is a fractal and attractive fixed set. It is one of the simplest fractals and is constructed iteratively.

To construct the Sierpinski triangle, one begins with an equilateral triangle. The midpoint of each side is found, and the three midpoints are connected to form a smaller equilateral triangle in the center. This central triangle is then removed. This process is repeated for the three remaining smaller equilateral triangles. At each iteration, the remaining triangles are divided into four smaller equilateral triangles, and the central one is removed. As this process is continued infinitely, the resulting shape is the Sierpinski triangle.

The Sierpinski triangle has many interesting properties. It has a fractal dimension of log(3)/log(2), which is approximately 1.585. This means that as one zooms into the fractal, the complexity of the pattern remains the same. It is also self-similar, meaning that any part of the triangle, when magnified, looks like the whole triangle. The Sierpinski triangle can be generated using an iterative function system. It also has connections to Pascal's triangle, where the entries modulo 2 form the Sierpinski triangle.