The Sierpinski Triangle

Sierpinski Triangle is an attractive triangle packed with unique attributes and attractive patterns in the field of fractal mathematics. This is Sierpinski's triangle, triangle fractal with zero area and infinite perimeter. There are many ways to create this triangle and there are many areas where it appears. Sierpinski Triangle named after Polish mathematician Waclaw Sierpinski has been the subject of research since Sierpinski discovered it for the first time in the early 20 th century.

For Sierpinski's triangle, we start with a solid triangle (2 dimensions). Next, delete the triangle in the middle of the solid triangle. You can make Sierpinski's triangle infinitely infinite time. I want to remove it from the triangle, so the size will be reduced. So, you reduce it from 2, but because it is not an approach line, you do not hit one. Therefore, the size is between 1 and. Approximate size is 5850

In an interview with Michael Silverblatt in 1996, David Foster Wallace acknowledged that the structure of the first draft of Infinite Jest by the editor Michael Pietsch was inspired by fractals, especially the Sierpinski triangle (Sierpinski gasket) "Balance Something like the bad Sierpinsky gasket. " If a circular boundary is drawn around a two-dimensional figure of a fractal, the scaling of each successive iteration of the fractal is smaller, so the fractal never crosses the boundary. When the fractal is repeated more than once, the perimeter of the fractal increases and the area does not exceed a certain value. The fractal in 3 dimensional space is similar, but the difference between 2 dimensional fractal and 3 dimensional fractal is that the 3 dimensional fractal increases the surface area, but does not exceed a certain volume.

C students see Sierpinski's triangle as an example of a fractal. Stage 0 is a shadowless triangle. To proceed to the first stage, get the three midpoints of the unshaded triangle edge, combine them and add a new triangle color in the middle. To obtain Stage 2, repeat this procedure for each triangle without shadows in the stage. This process continues indefinitely. Students record the number of unshaded triangles at each stage, look for patterns, and use the results to create a table to predict the number of unshaded triangles in 10 and 20 steps To do.