Title: Dimension Spectra of Lines,
Abstract: This paper investigates the algorithmic dimension spectra of lines in the
Euclidean plane. Given any line L with slope a and vertical intercept b, the
dimension spectrum sp(L) is the set of all effective Hausdorff dimensions of
individual points on L. We draw on Kolmogorov complexity and geometrical
arguments to show that if the effective Hausdorff dimension dim(a, b) is equal
to the effective packing dimension Dim(a, b), then sp(L) contains a unit
interval. We also show that, if the dimension dim(a, b) is at least one, then
sp(L) is infinite. Together with previous work, this implies that the dimension
spectrum of any line is infinite.