## Smart answer:

# Your search for *′What are fractals′* returned the following results:

### natural phenomena or mathematical sets of infinitely complex patterns that are self-similar across different scales

Fractals are natural phenomena or mathematical sets of infinitely complex patterns that are self-similar across different scales.

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### infinitely complex patterns that are self-similar across different scales, across different dimensions

Fractals are infinitely complex patterns that are self-similar across different scales, across different dimensions.

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### infinitely complex patterns that are self-similar across different scales, created by repeating a simple process over and over in a loop

Fractals are infinitely complex patterns that are self-similar across different scales, created by repeating a simple process over and over in a loop.

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### infinitely complex patterns — that are self-similar across different scales, formed from chaotic equations in other words, beautiful natural patterns that break into smaller sections that are similar to the original

Fractals are infinitely complex patterns that are self-similar across different scales, formed from chaotic equations — in other words, beautiful natural patterns that break into smaller sections that are similar to the original.

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### geometric objects that exhibit complex structure at every scale

Fractals are geometric objects that exhibit complex structure at every scale.

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### the pervasive and universal shapes, the fundamental geometric ‘words’ out of which the Book of Nature, as Galileo put Nature

In short, fractals are the pervasive and universal shapes, the fundamental geometric ‘words’ out of which the Book of Nature, as Galileo put Nature, is written.

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### beautiful, never-ending patterns that are found in nature, consisting of subsets that are similar to each other and to the parent pattern

Fractals are beautiful, never-ending patterns that are found in nature, consisting of subsets that are similar to each other and to the parent pattern.

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### self-similar patterns, where self-similar means they are the same from near as from far Fractals

The mathematical definition of a fractal also says something similar: Fractals are typically self-similar patterns, where self-similar means they are the same from near as from far Fractals may be the same at every scale.

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### spaces whose Hausdorff dimension strictly exceeds the topological dimension.[5

Fractals often are spaces whose Hausdorff dimension strictly exceeds the topological dimension.[5]

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### the visual depictions of mathematical equationsthe same equations

Fractals are the visual depictions of mathematical equationsthe same equations, in fact, that describe natural phenomena such as coastlines, plant shapes and weather patterns.

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