Fractals in Nature

[dragonfly]

Hello,

I am a biologist working with slime moulds that appear (to my eye, anyway) to be approximately fractal. I would like to quantify this observation, but realised I don't know of any test that will quantify whether or not my critter counts as fractal. I have been using fractal dimension, D (used box-counting method) to quantify growth under different conditions. So I have two real questions:
1. How do you quantitatively know that some object is fractal?
2. Can you use fractal dimension for objects that fail the test (assuming there is one)?

Thank you in advance for your help!!
Cheers,
Dragonfly

[lycium]

welcome to the forum 

i suppose the most "robust" answer to that problem is if the image can be well-represented by a fractal "compression" (reconstruction) algorithm; there will definitely be a quantitative difference between highly unstructured and fractal-structured images expressed in such a framework.

so, perhaps a starting point would be to read about the collage theorem

[David Makin]

Hello and welcome,

If your slime moulds are fractal then you may find that different varieties of slime mould will have distinct fractal dimension values when the box counting algorithm is applied - which could be a useful tool for identification purposes - then again all slime moulds may exhibit the same fractal dimension

It's possible that the closest fractal algorithm to slime mould growth is "Diffusion Limited Aggregation" - see:

http://mx.coldstorageonline.com/index.php?bid=53

bye
Dave

[David Makin]

For anyone interested I've done a fractal algorithm "DLA Inspired" for Ultra Fractal 5, it's a class formula - just set your main formula to mt.ufm-Pixel and then choose either "Generic Coloring (Gradient) render=false" or "Generic Coloring (Direct) render=false" from mmf5.ucl

[Nahee_Enterprises]

WOW YOU ARE A BIOLOGIST AR?  ITS REALLY GOOD...
YOU MUST BE KNOW MORE ABOUT FRACTALS IN NATURE...
PLEASE GIVE ME MORE INFORMATION ABOUT IT...

Greetings, and Welcome to this particular Forum !!!     

I am afraid that Tanya L. (dragonfly) only posted that one item to this forum back on August 05, 2008, and has not come back since then.  So you may not be getting any more information from her.

But you may ask specific questions concerning fractals and nature in the following Board:
    http://www.fractalforums.com/fractals-in-nature/
Or read the various topics already there.