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The Sierpinski triangle, also known as the Sierpinski gasket, is a fractal and attractive fixed set. It is a common example of a self-similar fractal, meaning it is exactly or approximately similar to a part of itself. The construction of the Sierpinski triangle begins with an equilateral triangle. The midpoints of the three sides are connected to form a smaller equilateral triangle in the center. This central triangle is then removed, leaving three smaller equilateral triangles. This process is then repeated indefinitely for each of the remaining triangles.

The Sierpinski triangle can be generated through various methods. One common iterative process involves starting with a solid triangle and repeatedly removing the central inverted triangle. Another method uses a matrix representation or a set of iterated function systems. Mathematically, it can be described using barycentric coordinates or by applying rules in a cellular automaton.

The fractal dimension of the Sierpinski triangle is approximately 1.585. This means that it is more complex than a one-dimensional line but less space-filling than a two-dimensional plane. Despite its fractal nature, the Sierpinski triangle has zero area in the limit of infinite iterations, as an infinite number of triangles with decreasing areas are removed. It is a classic example used in geometry, computer graphics, and chaos theory to illustrate concepts of fractals and self-similarity.