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Use the following iterations (or steps) to create a famous fractal based on the equilateral triangle called the Sierpinski triangle. Iteration 1: • Using a centimeter ruler, find the midpoint of each side of the triangle. • Connect the midpoints to form an inverted (upside-down) triangle in the middle. • Color in this triangle. Iteration 2:
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.
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.
Let’s draw the first three iterations of the Sierpinski’s Triangle! Iteration 1: Draw an equilateral triangle with side length of 8 units on triangular grid paper. Use the bottom line of the grid paper to draw the base of this triangle. Mark the midpoints of the three sides.
Fractals III: The Sierpinski Triangle. The Sierpinski Triangle is a gure with many interesting properties which must be made in a step-by-step process; that process is outlined below. Stage 0: Begin with an equilateral triangle with area 1, call this stage 0, or S0. (This is pictured below.)
This activity allows the user to step through the process of building the Sierpinski's Triangle. This activity is meant to show how changing the shape but using the same idea for a generator in a geometric fractal can yield a predictable final product.
One of the fractals we saw in the previous chapter was the Sierpinski triangle, which is named after the Polish mathematician Wacław Sierpiński. It can be created by starting with one large, equilateral triangle, and then repeatedly cutting smaller triangles out of its center.
