  This work tests if the large-scale galaxy distribution can be characterized
as a fractal system. The $\Lambda$CDM cosmology with $H_0=(70\pm 5)$ km/s/Mpc
is adopted to study the UltraVISTA DR1, COSMOS2015 and SPLASH surveys,
alongside the number density equations of these galaxy distribution systems as
fractals with dimension D. The relativistic distance definitions $d_L$, $d_Z$
and $d_G$ are used to estimate the galaxy number densities in the redshift
interval $0.1 \leq z \leq 4$ at volume limited subsamples. Applying the
appropriate relations for the description of galaxy fractal structures with
single dimension $D$ in the relativistic settings to these surveys datasets it
is possible to state that for $z<1$ the UltraVISTA DR1 galaxies presented an
average of $D=(1.58\pm 0.20)$, the COSMOS2015 galaxies produced $D=(1.39\pm
0.19)$ and the SPLASH galaxies generated $D=(1.00\pm 0.12)$. For $1 \leq z \leq
4$ the dimensions respectively decreased to $D=(0.59\pm 0.28)$,
$D=0.54^{+0.27}_{-0.26}$ and $D=0.83^{+0.36}_{-0.37}$. These results are robust
under the Hubble constant uncertainty assumed here. Analysis of blue and red
galaxies subsamples in the COSMOS2015 and SPLASH surveys show that the fractal
dimensions of blue galaxies present essentially no alteration from the values
above, although the ones for the red galaxies changed mostly to smaller values,
meaning that D may be assumed as a more intrinsic property of the distribution
of objects in the Universe, thus allowing for the fractal dimension to be used
as a tool to study different populations of galaxies. All results confirm the
decades old theoretical prediction of a decrease in the fractal dimension for
$z>1$ suggesting that either there are yet unclear observational biases causing
such decrease in the fractal dimension, or the galaxy clustering was possibly
more sparse and the universe void dominated in a not too distant past.
