Question is a Logarithm just a way to represent a multidimensional array?
IE Log^2 (8) = 3
shows 2 X 2 X 2 =8
two by two is a two dimensional box
Two by 2 by 2 iby 2 is a cube
What is a log with a not round number - a partial dimensional shift (Fractal dimension) The plot would not be symmetrical as in the round number but would warp out in a fractal plane/angle that was not a 90 degree angle . This would create the spirals of the known fractal patterns.