Sierpinski Triangle: Fractal Dimension

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This video continues with the fractal known as the Sierpinski Triangle. This fractal has an area equal to zero and fractional dimension approximately equal to 1.585.

The dimension can be found using an equation derived from a previous video (   • Fractal Dimension  ). Notice that each step scales the side lengths by 1/2 and three new triangles are formed, leading to the equation 2^D = 3, where D is the dimension of the fractal.

The Sierpinski triangle is formed when starting with a triangle, usually equilateral, and finding the midpoint of each side length. The midpoints are then connected with lines, forming four smaller triangles. The middle triangle is then removed. This process is then repeated infinitely many times, always finding the midpoints, connecting them with lines, and then removing the middle triangle, leaving three smaller, identical triangles.


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