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what is a fractal
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GPT-4o mini
A fractal is a complex geometric shape that can be split into parts, each of which is a reduced-scale copy of the whole. This property is known as self-similarity. Fractals are often found in nature, where they describe structures such as coastlines, mountains, clouds, and trees, which display intricate patterns and detail at various scales.
Fractals can be created mathematically and typically involve iterative processes, meaning that simple rules are applied repeatedly to generate intricate patterns. Some well-known examples of fractals include:
- **Mandelbrot Set**: A famous fractal that exhibits highly detailed and complex boundary structures.
- **Sierpinski Triangle**: Formed by recursively removing triangles from a larger triangle.
- **Koch Snowflake**: Created by adding smaller triangles to the sides of a larger triangle to create an infinitely detailed outline.
Fractal geometry is also used in various fields such as computer graphics, nature modeling, and the analysis of phenomena in physics, biology, and economics.
Fractals can be created mathematically and typically involve iterative processes, meaning that simple rules are applied repeatedly to generate intricate patterns. Some well-known examples of fractals include:
- **Mandelbrot Set**: A famous fractal that exhibits highly detailed and complex boundary structures.
- **Sierpinski Triangle**: Formed by recursively removing triangles from a larger triangle.
- **Koch Snowflake**: Created by adding smaller triangles to the sides of a larger triangle to create an infinitely detailed outline.
Fractal geometry is also used in various fields such as computer graphics, nature modeling, and the analysis of phenomena in physics, biology, and economics.
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