What is the Dimension of This Cellular Fractal?

  • Thread starter Thread starter bogdan
  • Start date Start date
  • Tags Tags
    Fractal
Click For Summary

Discussion Overview

The discussion revolves around the dimension of a cellular fractal generated using specific rules and parameters. Participants explore the properties of the fractal, including its visual representation and mathematical estimation of its dimension.

Discussion Character

  • Exploratory
  • Mathematical reasoning

Main Points Raised

  • One participant shares a link to an image of the fractal, although others report issues accessing it.
  • Another participant suggests that the fractal is related to John Conway's game.
  • A later post provides a mathematical approach to estimating the fractal's dimension using the equation N=CrD, proposing a dimension of approximately 1.46 based on specific parameters.

Areas of Agreement / Disagreement

Participants express differing experiences with accessing the fractal image, and while there is a mathematical estimation presented, the discussion does not reach a consensus on the dimension or its implications.

Contextual Notes

The estimation of the fractal's dimension relies on specific parameters and assumptions about the sampling circle and fundamental units, which may not be universally applicable.

bogdan
Messages
188
Reaction score
0
Nice...isn't it ?
http://www.angelfire.com/pro/fbi/fractcell.bmp

Generated with life32, rule V:s01234/b13 and one original cell...generation 440...zoom 1/2...
 
Last edited by a moderator:
Mathematics news on Phys.org
Erm... the link is broken for me.
 
john conway's game if I am not mistaken.
 
The page you are looking for has spontaneously combusted.
Actually, we couldn't find the page you requested. Please check the URL

--EDIT-- Ok its weird..sometimes its broken..but it just worked for me..here..I uploaded it to my account..Voila
http://home.attbi.com/~dav2008/images/fractcel.JPG
 
Last edited by a moderator:
The dimension of this fractal may be estimated by using the equation N=CrD, where N=number of fundamental units of replication, C is a constant, r is the radius of a "sampling circle," and D is the dimension of the fractal. For this fractal, a factor of three radii increases the fundamental units bounded by the circle by approximately five, yielding N=5=3D, and a dimension of approximately 1.46. (Scientific American.)
 

Similar threads

  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 6 ·
Replies
6
Views
3K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 7 ·
Replies
7
Views
6K
  • · Replies 4 ·
Replies
4
Views
4K
  • · Replies 10 ·
Replies
10
Views
2K
  • · Replies 5 ·
Replies
5
Views
10K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K