Fractals: Infinite Perimeters & Plank Scale

  • Thread starter Thread starter freerangequark
  • Start date Start date
  • Tags Tags
    Fractals Infinite
Click For Summary
Fractals are mathematical constructs characterized by self-similarity and can theoretically possess infinite perimeters. However, in the physical world, actual fractals cannot exhibit infinite lengths due to limitations imposed by the Planck scale, which represents the smallest measurable length where quantum effects become significant. The discussion highlights the distinction between mathematical ideals and physical realizations, noting that true fractals do not exist in nature. The Planck length is defined using fundamental constants, indicating a boundary where classical physics transitions to quantum mechanics. Ultimately, while fractals can have infinite perimeters mathematically, physical constraints prevent their realization in the real world.
freerangequark
Messages
16
Reaction score
0
Are the perimiters of fractals infinite? Or does Plank scale prohibit that?

Thanks,
FRQ
 
Physics news on Phys.org
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
 

Attachments

  • planck.png
    planck.png
    1.3 KB · Views: 504
Last edited:

Thread 'Is this a coincidence?... (distances between planets)'

I'm not a student or graduate in Astrophysics.. Wish i were though... I was playing with distances between planets... I found that Mars, Ceres, Jupiter and Saturn have somthing in common... They are in a kind of ratio with another.. They all got a difference about 1,84 to 1,88x the distance from the previous planet, sub-planet. On average 1,845x. I thought this can be coincidential. So i took the big moons of Jupiter and Saturn to do the same thing jupiter; Io, Europa and Ganymede have a...
View full post »

Similar threads

Undergrad MOND from galaxies that are fractal
  • · Replies 10 ·
Replies
10
Views
2K
Undergrad Expressing any given point on plane with one unique number
  • · Replies 4 ·
Replies
4
Views
2K
Fractal geometry in crumpled paper
  • · Replies 1 ·
Replies
1
Views
3K
Undergrad Is Spacetime infinite dimensional?
  • · Replies 9 ·
Replies
9
Views
2K
Is fractal nature dependent on the number of steps?
  • · Replies 6 ·
Replies
6
Views
2K
Undergrad Scale Factors: Is a 10x Bigger Earth Possible?
  • · Replies 3 ·
Replies
3
Views
1K
Undergrad Degrees of Freedom in Lagrangian Mechanics for a Fractal Path
  • · Replies 2 ·
Replies
2
Views
1K
How Are Fractals Related to Chaos?
  • · Replies 11 ·
Replies
11
Views
7K
High School What is the Area of a Sierpinski Triangle?
  • · Replies 7 ·
Replies
7
Views
5K
Is the Universe a Fractal Structure Revealing Infinite Scales?
  • · Replies 5 ·
Replies
5
Views
6K