Fractals: Infinite Perimeters & Plank Scale

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SUMMARY

Fractals are mathematical constructs characterized by infinite perimeters, which exist independently of physical limitations. The discussion highlights the distinction between mathematical fractals and their physical realizations, emphasizing that true fractals do not manifest in the physical world due to constraints like the Planck scale. The Planck length, defined by fundamental constants such as Planck's constant, the gravitational constant, and the speed of light, represents the scale at which quantum gravity effects become significant, further complicating the relationship between fractals and physical reality.

PREREQUISITES
  • Understanding of fractals and their mathematical properties
  • Familiarity with the concept of the Planck length
  • Knowledge of fundamental physical constants (Planck's constant, gravitational constant, speed of light)
  • Basic grasp of quantum gravity principles
NEXT STEPS
  • Research the mathematical properties of fractals, focusing on their infinite perimeters
  • Study the implications of the Planck length in quantum gravity
  • Explore the relationship between mathematical models and physical representations of fractals
  • Examine the role of fundamental constants in defining the Planck scale
USEFUL FOR

Mathematicians, physicists, and students interested in the intersection of mathematics and physics, particularly those exploring fractals and quantum gravity concepts.

freerangequark
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Are the perimiters of fractals infinite? Or does Plank scale prohibit that?

Thanks,
FRQ
 
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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.

Please define fractals for me.
 
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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