Sierpiński gasket
Quick Summary
Polish mathematician Wacław Sierpiński described the fractal that bears his name in 1915, although the design as an art motif dates at least to 13th-century Italy. Begin with a solid equilateral triangle, and remove the triangle formed by connecting the midpoints of each side. The midpoints of the sides of the resulting three internal triangles are connected to form three new triangles that are then removed to form nine smaller internal triangles. The process of cutting away triangular pieces continues indefinitely, producing a region with a Hausdorf dimension of a bit more than 1.5 (indicating that it is more than a one-dimensional figure but less than a two-dimensional figure).
The Sierpiński gasket is a fractal, a complex geometric shape with a "fractional dimension". It is created by starting with an equilateral triangle, dividing it into four smaller congruent triangles, and removing the central one. This process is then repeated on the remaining three triangles, and so on.12
Key characteristics of the Sierpiński gasket include:
* Self-similarity: Small parts of the gasket resemble the whole shape.2
* Zero area: Despite its intricate structure, the gasket has no area.2
* Fractional dimension: Its dimension is between that of a line (one-dimensional) and a plane (two-dimensional).2
* Infinite boundary length: The edges of the gasket are infinitely long.2
Fractals, a concept developed by mathematicians like Benoit Mandelbrot, are used to model irregular natural phenomena and have applications in various scientific fields.1
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