How do you construct a Sierpinski triangle?
How do you construct a Sierpinski triangle?
Constructing the triangle is fairly straightforward: Step One: Draw a triangle (typically equilateral). Step Two: Draw a point in the middle of each of the three sides of the triangle, and then connect those points to form a new triangle. Now we have four smaller triangles, one in the middle and three in the corners.
What is the dimension of the Sierpinski carpet?
1.8928
Sierpinski carpet The dimension of the carpet is log 8 / log 3 = 1.8928. Note that any line between two adjacent vertices of the gasket is a triadic cantor set. Fractal antenna based upon the carpet replaces the usual rubbery stalk.
How many triangles are in Sierpinski gasket?
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.
What is the area of the Sierpinski gasket?
Area of the Sierpinski Gasket To get S(k+1), we scale S(k) by 1/2, which reduces the area by 1/4 = (1/2)2. But we make 3 copies of this scaled version to form S(k+1). Therefore the area of S(k+1) must be (3/4)th of the area of S(k).
How do you make a Sierpinski gasket?
The Sierpinski triangle may be constructed from an equilateral triangle by repeated removal of triangular subsets:
- Start with an equilateral triangle.
- Subdivide it into four smaller congruent equilateral triangles and remove the central triangle.
- Repeat step 2 with each of the remaining smaller triangles infinitely.
How many dimensions is a Sierpinski triangle?
The Sierpinski tetrahedron or tetrix is the three-dimensional analogue of the Sierpinski triangle, formed by repeatedly shrinking a regular tetrahedron to one half its original height, putting together four copies of this tetrahedron with corners touching, and then repeating the process.
What is Sierpinski’s triangle used for?
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.
