I fail to see how the planting patterns are fractal. A fractal pattern is one which repeats itself at different scales. I realize that the repetition does not need to be exact but I don't see how there is any at all in this situation.
EDIT: I'm actually just learning about fractals, so I'm certainly no expert, but I'm excited to share what I've learned so far.
Look at a line, square, and cube in 1, 2, and 3 dimensions respectively. If you scale down each by 1/2 in all its dimensions, you need to look at how much of the "mass" (for lack of a better term is scaled down
If you cut a line in 1/2, it's mass is scaled by 1/2 as it takes 2 one-half length lines to make the original line.
If you scale a square down 1/2 along all its dimensions, you break into/scale it down into 4 smaller squares, it's mass scaling factor is 1/4....scaling a cube down 1/2 along all its dimensions (1/2)^2 breaks it into 8 smaller cubes...it's scaling factor is 1/8 and you can see the progression here. (1/2)^3. (I imagine a tesseract/hypercube has a scaling of 1/16 as it is the 4D analogue of a cube) The exponent represents the concept of dimension and this is how you can have non-integer dimensions.
So, back to the Sierpenski triangle or triforce example. Let's scale it down 1/2. When we do that, we know we get 1/3 the "mass" of the original since there are 3 triangles contained in the larger triangle at each level. The dimensionality is then (1/2)^x = 1/3 where x is the dimensionality. We rewrite this as log 3 base 2 which gives it a dimensionality of ~1.585.
And that is the definition of a fractal, a shape with a non-integer dimension which gives the shape roughness at every scale. I don't quite understand the more technical definition, but hopefully this helps!
Note, you cannot use length or area as a measurment for a scaling factor, as the length would be infinite and area would be 0. Also, I say mass because the more correct concept is difficult for me to explain without a whiteboard, but basically, it has to do with putting the fractal on a 2d grid, scaling it, and seeing what the ratio of boxes touched is. See, told you I'm bad at explaining it :D
Off topic, but does anyone know how this would affect the Fermi Paradox if aliens produce technology inherently fractal in nature?
And that the fractal dimension is usually equivalent to the mincowski dimension (the limit of the area measured by finite boxes as the size of the boxes grows arbitrarily small) and hausdorf dimension (the limit of the perimeter as measured by an aproximting polygon with equal length sides as the number of sides grows arbitrarily large) along with others.