# Understanding the expression of fractal dimension in plants

I just finished a small, demo exercise on fractal dimension of a plant by using MATLAB and box-count method. There were two different treatments. A plant treated with a specific hormone and a plant without treated with anything.

Above there are the initial pictures of these plants [treated and untreated].

Here are the logarithmic plots for these two treatments

Finally i got the derivatives of ln(N)/ln(R) and as you can see :

So after all these photos the fractal dimension of treated plant was 1.8853 and the dimension of the untreated was 1.9322

So i would like to understand what these two number expressing. Can we get a conclusion about these two different treatments ?

Also in the derivative plots. What the (kind-of) lineal part of the function means ? Can we say that in these regions our image acts like a fractal?

When the log-log plot of $n(r)$ is approximately linear, this means that the number of boxes covering the set grows as some power of $r$, that is $n(r)\approx Cr^{-d}$. This is an indication of the set having box-counting (Minkowski) dimension equal to $d$. Yes, you can say that in this range of scales $r$ the image looks like a fractal.