If you have a square(just follow along with this), and you wanted to know how many more squares you would need to make it 2, 3 or 4 times as big, you would take the scaling factor and put it to the exponent of the dimension.
3^2(a square three times as big)
... and this applies to other dimensions as well. How many more cubes would you need to make it 4 times as big? 4^3

scaling factor^dimension = number of copies


So if we take a fractal, such as the Sierpinski triangle and ask ourselves: what dimension does it exist in? We would have to figure out two things: the scale, and the number of copies of that make it that scale. Making a Sierpinski triangle is a iterative process. Check out the link:
http://en.wikipedia.org/wiki/Sierpinski_triangle

To make a Sierpinski triangle twice as big, you take 3 trianges and place 2 underneath the first. So to double a Sierpinski triangle in size, you need 3 copies of that triangle. So using our equation...

2^d = 3
dimension = 1.58........

i just heard this from a mathematics phd



i just found this wikipedia page:
http://en.wikipedia.org/wiki/List_of_fractals_by_Hausdorff_dimension

apparently, it's called a Hausdorff dimension
http://en.wikipedia.org/wiki/Hausdorff_dimension

This post was edited by finiteinfinity on Feb 25 2009 01:47am

this does not amuse or interest me, this bores me, this^