Sierpinski Triangles

Sierpinski triangles, sometimes called Sierpinski gaskets, are a type of fractal shape that is named after Polish mathematician Waclaw Sierpinski. It is a mathematical construct, which is created by removing smaller triangles from an equilateral triangle in a specific pattern. To create a Sierpinski triangle, you begin with an equilateral triangle and divide it in the center to create three smaller triangles, with one triangle pointing upwards and the other two pointing downwards. Next, you remove the middle triangle to create a shape that looks like a smaller equilateral triangle with an upside-down equilateral triangle on top of it. This process is repeated for each smaller triangle created, recursively removing the center triangle in every iteration, to create a pattern that looks like a fractal with smaller and smaller triangles. Sierpinski triangles have a number of interesting mathematical properties, such as being self-similar, having a fractal dimension of 1.585, and containing an infinite number of smaller triangles, each of which is a scaled-down version of the larger triangle. Sierpinski triangles have also been used in fields outside of mathematics, such as in architecture and graphic design, where they are used to create visually interesting geometric patterns. The Sierpinski triangle is a simple example of a fractal, which is a mathematical object or set that exhibits selfsimilarity at various scales and has a simple iterative algorithm.

Sierpinski triangles have been used as a design inspiration in architecture to create visually interesting patterns, particularly on facades of buildings. One example of the use of the Sierpinski triangle in architecture is the Delft University of Technology Library in the Netherlands, designed by Dutch architect Mecanoo. The facade of the library features a repeating pattern of equilateral triangles, with some of the triangles removed in a pattern that resembles a Sierpinski triangle. The resulting pattern is a visually striking arrangement of positive and negative space that creates a sense of depth and texture.