# Fractals: Infinite Perimeters & Plank Scale

• freerangequark
In summary, fractals are mathematical objects with infinite length perimeters, but they cannot be realized physically due to the limit on length. The Planck length, which is the length scale at which quantum gravity is apparent, may be connected to fractals and has a formula involving Planck's constant, the gravitational constant, and the speed of light. However, true fractals do not seem to exist in the physical world.
freerangequark
Are the perimiters of fractals infinite? Or does Plank scale prohibit that?

Thanks,
FRQ

You are confusing physics and mathematics. Fractals are mathematical objects, so there is no problem with having infinite length perimeters. If you tried to realize it physically, there is a limit on length.

I am interested to know what is meant by Plank scale and whether the perimeters of fractals are infinite.

The boundary of fractals are infinite.

The Planck length is thought to be the length scale at which quantum gravity is apparent.

True fractals do not seem to be found in the physical world, therefore they have no simple connection with quantum gravity or the Planck scale.

I found this formula definition of the Planck length for you:

where,
h-bar = Plank's constant

G = Gravitational constant

C = Speed of light in vacuo

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## 1. What are fractals?

Fractals are geometric shapes or patterns that repeat at different scales, creating self-similarity. They are considered to have infinite complexity and can be found in nature and in mathematical equations.

## 2. How do fractals have infinite perimeters?

Fractals have infinite perimeters because as you zoom in closer to a fractal shape, more and more detail is revealed. This means that the perimeter of the shape keeps increasing as you zoom in, never reaching a finite value.

## 3. How are fractals related to the Plank scale?

The Plank scale is the smallest possible unit of length in the universe, and fractals are geometric patterns that can be infinitely small. Some scientists believe that the structure of the universe at the Plank scale may be fractal-like.

## 4. How are fractals useful in science?

Fractals have many applications in science, including in the study of chaos theory, weather patterns, and the growth of natural systems such as trees and coastlines. They can also be used in data compression, image processing, and creating realistic computer graphics.

## 5. Can fractals be used to model real-world phenomena?

Yes, fractals have been used to model a wide range of real-world phenomena, including the stock market, population growth, and the behavior of fluids. They can also be used to create more accurate simulations of natural systems and phenomena.

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