Fractals vs Self-similar

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Fractals vs Self-similar

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ช่วยง่ายที ที่ซึ้ง ถึงพื้นฐาน
รีบรีบตอบ อย่าได้ ให้คอยนาน
ดำเนินการ พร้อมยก ตัวอย่างแสดง

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In mathematics, a fractal is a self-similar subset of Euclidean space
whose fractal dimension strictly exceeds its topological dimension.

Fractals appear the same at different levels, as illustrated in
successive magnifications of the Mandelbrot set.[1][2][3][4]

Fractals exhibit similar patterns at increasingly small scales called self-similarity,
also known as expanding symmetry or unfolding symmetry;
if this replication is exactly the same at every scale, as in the Menger sponge,[5]
it is called affine self-similar.

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In mathematics, a self-similar object is exactly or approximately similar to a part of itself
(i.e., the whole has the same shape as one or more of the parts).

Many objects in the real world, such as coastlines, are statistically self-similar:
parts of them show the same statistical properties at many scales.[2]

Self-similarity is a typical property of fractals.

Scale invariance is an exact form of self-similarity where at any magnification
there is a smaller piece of the object that is similar to the whole.

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