Fractals: Infinite Perimeters & Plank Scale

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Discussion Overview

The discussion revolves around the nature of fractals, specifically whether their perimeters can be considered infinite and how this concept relates to the Planck scale. Participants explore the mathematical properties of fractals and their implications in physical reality.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Mathematical reasoning

Main Points Raised

  • One participant questions if the perimeters of fractals are infinite or if the Planck scale imposes a limit on this idea.
  • Another participant asserts that fractals are mathematical constructs, allowing for infinite perimeters without physical constraints, but acknowledges that physical realizations would encounter limitations.
  • A participant expresses interest in understanding the Planck scale and requests a definition of fractals.
  • Links to external resources are provided for further reading on fractals.
  • It is stated that the boundaries of fractals are infinite, and the Planck length is described as the scale where quantum gravity effects become significant.
  • One participant suggests that true fractals do not exist in the physical world, indicating a disconnect between mathematical fractals and physical phenomena like quantum gravity.
  • A formula for the Planck length is mentioned, referencing fundamental constants but without further elaboration.

Areas of Agreement / Disagreement

Participants express differing views on the relationship between mathematical fractals and physical reality, particularly regarding the implications of the Planck scale. There is no consensus on whether true fractals can exist in the physical world.

Contextual Notes

Limitations include the lack of clarity on how the Planck scale interacts with fractal geometry and the assumptions underlying the definitions of fractals and their physical realizations.

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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