Why are fractals important? Fractals help us study and understand important scientific concepts, such as the way bacteria grow, patterns in freezing water (snowflakes) and brain waves, for example. Their formulas have made possible many scientific breakthroughs.

A fractal often has the following features:

• It has a fine structure at arbitrarily small scales.
• It is too irregular to be easily described in traditional Euclidean geometric language.
• It is self-similar (at least approximately or stochastically).

Where To Observe Fractals In Nature: Walking through a forest, you will find fractal patterns in the network-like branching patterns everywhere among the ferns, trees, roots, leaves, and the fungal mycelium in the soil.

You can clearly imagine how a volume with a fractal surface could have an infinite surface. However, a fractal shape like the Koch snowflake curve does not, in general, have an infinite area.

The surface area enclosed by the fractal depends on the shape and size of the fractal (and if it is closed), as with any other shape. For fractals in 3D space (or higher) with topological dimension 2, i.e. surface fractals, then their surface area is infinite: from Exploring Scale Symmetry .

A Fractal is a type of mathematical shape that are infinitely complex. In essence, a Fractal is a pattern that repeats forever, and every part of the Fractal, regardless of how zoomed in, or zoomed out you are, it looks very similar to the whole image.

FractalsThe Sierpinski Triangle. The Sierpinski triangle is a self-similar fractal. It consists of an equilateral triangle, with smaller equilateral triangles recursively removed from its remaining area.

The Koch snowflake (also known as the Koch curve, Koch star, or Koch island) is a fractal curve and one of the earliest fractals to have been described.

Cantor set, Sierpinski carpet, Sierpinski gasket, Peano curve, Koch snowflake, Harter-Heighway dragon curve, T-Square, Menger sponge, are some examples of such fractals.

The theoretical fractal dimension for this fractal is 5/3 ≈ 1.67; its empirical fractal dimension from box counting analysis is ±1% using fractal analysis software.

you get a fractal called Sierpinski’s triangle. Fractals can be found all over the place, in nature or in math. It does go on and on and on and on forever because there is no true limit to the iterations that can go into a fractal.

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A fractal is a never-ending pattern. Fractals are infinitely complex patterns that are self-similar across different scales. They are created by repeating a simple process over and over in an ongoing feedback loop.

10 Answers. One can have a bounded region in the plane with finite area and infinite perimeter, and this (and not the reverse) is true for (the inside of) the Koch Snowflake.

A shape that has an infinite perimeter but finite area.

has infinite length between x = 0 and any other point, say P. So if you draw a connecting line between P and the origin which does not cross or touch the curve, you have a shape with infinite perimeter enclosing a finite area.

Anything multiplied by zero equals zero, so the area of a rectangle is zero if either its length or its width or both is/are zero. LONG ANSWER: In that case, though, it is dubious that it can still be called a rectangle.