How is the Sierpinski triangle a fractal?

How is the Sierpinski triangle a fractal?

The Sierpinski triangle is a self-similar fractal. It consists of an equilateral triangle, with smaller equilateral triangles recursively removed from its remaining area. It can be created by starting with one large, equilateral triangle, and then repeatedly cutting smaller triangles out of its center.

How do you make a Sierpinski tetrahedron?

It can be formed in many ways: (1) start with a single tetrahedron and remove octahedra from it, (2) recursively combine quadruples of tetrahedra into larger tetrahedra, (3) take “Pascal’s Pyramid” of trinomial coefficients modulo two, (4) form the graph of the binary exclusive-or function on the unit square.

What is the pattern of Sierpinski triangle?

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 do you make a fractal tree?

Fractal tree

1. Draw the trunk.
2. At the end of the trunk, split by some angle and draw two branches.
3. Repeat at the end of each branch until a sufficient level of branching is reached.

What is a fractal tetrahedron?

A tetrahedron is a three-dimentional solid made of four triangles. Each student will create their own fractal tetrahedron out of toothpicks and mini-marshmallows. Students will then group together in teams of four and combine their tetrahedrons into a larger version of the same shape.

How do you make a fractal cut out card?

What to do

1. Fold one piece of card in half.
2. Mark a point half way along the fold.
3. Cut along the line.
4. Unfold the card and push the flap inside the card as in the diagram.
5. Fold the card flat.
6. Mark a point halfway along each fold.
7. Cut along each line.
8. Unfold the card and push these flaps inside the card as in the diagram.

How do you identify fractals?

The rules for identifying fractals are as follows:

1. A bearish turning point occurs when there is a pattern with the highest high in the middle and two lower highs on each side.
2. A bullish turning point occurs when there is a pattern with the lowest low in the middle and two higher lows on each side.

What is a fractal algorithm?

A Fractal is a never-ending pattern. Fractals are infinitely complex patterns that are self-similar across different scales. They are created by repeating a simple process over and over in an ongoing feedback loop. Mathematically fractals can be explained as follows.

How is the Sierpinski triangle an example of a fractal?

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 do you draw a Sierpinski triangle with a ruler?

With pencil and ruler, find the midpoints of each side of the triangle and connect the points. Additional Steps to Draw a Sierpinski Triangle Now repeat the process with the three “outside” triangles of the figure.

How do you make a triangle in a fractal?

1. Draw axes close to left and bottom side of the paper. 2. Pick three points to make a large triangle. It will be easier if one of the points is the origin and one of the points lies on one of the axes. Do not try to make a right or equilateral triangle.

What was the purpose of the Sierpinski triangle project?

Louis Sievers Trinity High School The purpose of this project is to explore Sierpinski triangles and the math behind them. They provide an introduction to fractals, and connections to computer graphics and animation. The activities also give practice in some geometric techniques and some tie-ins to geometric theorems.