Sierpinski Triangle is one of the most famous fractals. There are 5 ways you can form it.
The Sierpinski triangle is a fractal cluster, which is formed by cutting out pieces of a triangle. To form it, you start with an equilateral triangle, divide it into 4 smaller triangles and cut out the center one:
If you do the same with each of the three triangles left and continue cutting out infinitely, you will get the following fractal:
BASE MOTIF METHOD
The Sierpinski Triangle can also be considered a base-motif fractal and can be formed by generator iteration with the following base and motif:
The other three ways the Sierpinski Triangle can be formed are using the midpoint method, IFS iteration, or the Sierpinski Curve. Read about these topics to find out.
The fractal dimension of the Sierpinski Triangle can be easily found using the similarity method. In this fractal, there are 3 identical triangles, each of which requires 2x magnification to become identical to the entire figure. The fractal dimension is then log 3 / log 2, which is approximately 1.58.
After every iteration, we only leave 3/4 of the area of the triangle. As we increase the number of iterations, the area will approach 0, and become so after an infinite number of iterations.
The Sierpinski Triangle is used in the Chaos game. Play it to find out more!