box count resolution is the slope ... right ?

[cKleinhuis]

i started my boxcounting software, and now i am unsure how to interpret the values,
i count the boxes on a fixed grid size, then i do the log log plotting as described here:
http://classes.yale.edu/fractals/fracanddim/boxdim/BoxDim.html

so, i have a few questions ...

1. the box counts "the border" meaning that full boxes are not counted in to the final result - thus the fractal dimension of the border is approximated ?
2. the box counting of a single square should then lead to a box counting dimension of exactly 1 ? sure, box counting is an approximation, but the result should come close to 1 ?
3. the box counting dimension is the slope of the line through consecutive points ?!

[lkmitch]

1. Yes, this method (in practice) approximates the dimension of the border, assuming you have a filled-in shape that is one color on the inside and another on the outside.
2. Yes, a square (outline) is just 4 straight line segments, so the dimension should be 1.
3. In practice, it's better to do a least-squares line fit, being careful with the points on either end.  Generally, the middle of your data should be linear on a log-log plot and will provide a better estimate.  Use the slope of the least-squares line, instead of point-to-point slopes.

[cKleinhuis]

thank you, the leastsquare lines seems to be suitable i am going to use this, and
in fact the dimension for a square is already close to 1...

lols, i want to test my haircut with it, as example, wishy washy hair like the dr. wisenhimers haircut should have a higher fractal dimension than the clean haircut of the newscaster