What is a Sierpinski Tetrahedron?

Page 1. Sierpinski Tetrahedron. A Sierpinski Triangle is a fractal based on an equilateral triangle, made by dividing the triangle into four smaller triangles, removing the central triangle and then repeating for each of the three remaining triangles. If you repeat this process forever, you get a fractal.

What is the formula for Sierpinski triangle?

We can break up the Sierpinski triangle into 3 self similar pieces (n=3) then each can be magnified by a factor m=2 to give the entire triangle. The formula for dimension d is n = m^d where n is the number of self similar pieces and m is the magnification factor.

What is the Sierpinski algorithm?

The Sierpinski triangle illustrates a three-way recursive algorithm. The procedure for drawing a Sierpinski triangle by hand is simple. Start with a single large triangle. Divide this large triangle into four new triangles by connecting the midpoint of each side.

How do you make a Sierpinski pyramid?

The Sierpinski triangle may be constructed from an equilateral triangle by repeated removal of triangular subsets:

  1. Start with an equilateral triangle.
  2. Subdivide it into four smaller congruent equilateral triangles and remove the central triangle.
  3. Repeat step 2 with each of the remaining smaller triangles infinitely.

Is a tetrahedron a fractal?

A tetrahedron is a simple three-dimensional shape made of four equilateral triangles. The basic building block of the fractal tetrahedron is made with four marshmallows and six toothpicks.

What is the purpose of Sierpinski triangle?

The Sierpinski triangle activity illustrates the fundamental principles of fractals – how a pattern can repeat again and again at different scales and how this complex shape can be formed by simple repetition. Each students makes his/her own fractal triangle composed of smaller and smaller triangles.

How many triangles are there in Sierpinski?

This leaves us with three triangles, each of which has dimensions exactly one-half the dimensions of the original triangle, and area exactly one-fourth of the original area. Also, each remaining triangle is similar to the original.

Is Sierpinski triangle a fractal?

FractalsThe Sierpinski Triangle. The Sierpinski triangle is a self-similar fractal. It consists of an equilateral triangle, with smaller equilateral triangles recursively removed from its remaining area.