Sabinsky carpet, also known as Sabinsky map, is an infinitely complex geometric figure. It was invented by Polish mathematician Scherbins based on 19 16, and it is a fractal-like figure. Shebinski carpet starts from a square, then divides it into 9 small squares, removes the middle square, and the remaining 8 squares are divided into 9 small squares, removes the middle square, and so on until it is infinitely subdivided. The final figure is a geometric figure with self-similarity, and its shape is similar to that of a carpet.

Operation steps of Scherbinsky carpet

To draw a Sabinsky carpet, you need to follow the following steps:

1. Draw a square and divide it into 9 small squares.

2. Remove the square in the middle.

3. Perform step 1 and step 2 respectively for the remaining 8 small squares.

4. Repeat step 3 until it is infinitely subdivided.

5. I finally got the Shebinski carpet.

Mathematical Properties of Scherbinsky Carpet

Shebinski carpet has many interesting mathematical characteristics. One of the most famous is its dimension. Although the Sabinsky carpet looks like a two-dimensional figure, its dimension is not an integer. In fact, the dimension of Scherbinsky carpet is a fraction between integer and two dimensions, namely 1.585.

This score shows that the Shebinski carpet has special properties between one and two dimensions. It has both one-dimensional self-similarity and two-dimensional morphology. This characteristic makes Scherbinsky carpet a classic example of fractal geometry.

Aesthetic Value of Scherbinsky Carpet

In addition to mathematical value, Shebinski carpet also has high aesthetic value. Its geometric form has the characteristics of simplicity, symmetry and aesthetic feeling, and it is a very beautiful figure. The self-similarity of Scherbinsky carpet makes it have a profound aesthetic feeling, which makes people feel the infinity and eternity of the universe.

The aesthetic value of Scherbinsky carpet is not only reflected in the geometric form, but also in its color. Shebinski carpets can be filled with various colors, and different filling methods can present different aesthetic feelings. The color change of Scherbinsky carpet can also be used to express abstract concepts such as emotion and artistic conception.