1. ## Loci vs. Fractal

Is there a connection between loci​ [in math] to fractal (patterns) [in physics]?!

2. ## Re: Loci vs. Fractal

"Loci" (plural of "locus") simply means sets of points that satisfy some condition. A "locus" can be as simple as a line or a circle. A set is "fractal" if it has fractional "generalized dimension" such as the "box counting dimension" or "information dimension".

3. ## An example of mine

Can be a connection between loci to Snowflake shape?!

4. ## Re: An example of mine

Originally Posted by policer
Can be a connection between loci to Snowflake shape?!
Not, perhaps, in the sense that you seem to be getting at. I'm sure you could find a fractal that has the appearance of a snowflake. But a fractal does not cover an area, nor does it contain straight lines. There is always a "texture" to the fractal: a straight line would break down into an infinitely detailed collection of "dots."

-Dan

5. ## Re: An example of mine

Originally Posted by topsquark
Not, perhaps, in the sense that you seem to be getting at. I'm sure you could find a fractal that has the appearance of a snowflake. But a fractal does not cover an area, nor does it contain straight lines. There is always a "texture" to the fractal: a straight line would break down into an infinitely detailed collection of "dots."

-Dan
I'm not sure I agree with this. I'm pretty sure the perimeter of a Koch snowflake is continuous.

6. ## Re: An example of mine

Originally Posted by romsek
I'm not sure I agree with this. I'm pretty sure the perimeter of a Koch snowflake is continuous.
Really? My bad then. Thanks for the catch.

-Dan