What is the pattern of the 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. Wacław Franciszek Sierpiński (1882 – 1969) was a Polish mathematician. The Sierpinski problem is trying to find the smallest Sierpinski numbers.

What is the fractal dimension of the Sierpinski triangle?

Since the Sierpinski Triangle fits in plane but doesn’t fill it completely, its dimension should be less than 2.

What is a fractal card?

Students make a 3-dimensional fractal cutout card by repeating a simple process of cutting and folding. They can turn their cutout into a fractal popup greeting card, decorate it artistically and share the lessons of fractals with others.

What are 3 well known fractals?

Cantor set, Sierpinski carpet, Sierpinski gasket, Peano curve, Koch snowflake, Harter-Heighway dragon curve, T-Square, Menger sponge, are some examples of such fractals.

What are four types of fractal patterns?

They are tricky to define precisely, though most are linked by a set of four common fractal features: infinite intricacy, zoom symmetry, complexity from simplicity and fractional dimensions – all of which will be explained below.

What is a fractal triangle?

Fractal Triangle. Each students makes his/her own fractal triangle composed of smaller and smaller triangles. Next, students cut out their own triangle and assemble them into a larger fractal pattern that replicates the same shape.

How do you make a fractal triangle bigger?

Next, join your fractal triangle with two other fractal triangles to form a bigger triangle. Then add two more groups of three triangles to form a bigger triangle made of nine triangles. If you’re doing this with your whole class, you can join three groups of nine to make a giant triangle made of 27 individual triangles.

What is a 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 smaller triangles can you make with 3 triangles?

Each of the three triangles now turns into three smaller triangles, leaving nine small white triangles. Connect the midpoints of each of the nine white triangles to form 27 smaller downward-pointing triangles. Color those in. Continue this process for as long as you like, creating triangles in factors of three: 81, 243 or even 729!