When interpreted in terms of a particular fractal model, regularities in the ratio of typical lengths and times between particles and galaxies are found which suggest that self-similarity between these two scales could exist. To establish the fractal model, we first review briefly some of the evidence pro and contra the local quasar hypothesis (LH). Forceful arguments have been advanced on both sides, whence we suggest, after others, that two classes of objects should be distinguished. A first class would be constituted of face-on giant elliptical radio galaxies and face-on Seyfert galaxies, with slight to moderate excess redshift. Those are called quasars in the mainstream literature. The second class would contain much smaller (about the size of a galaxy nucleus), faint and compact objects with large excess redshift, which we propose to call Compact Excess Redshift Objects (CEROs). The latter would be emitted by the nuclei of giant spiral and elliptical galaxies. A Unified Ejection Scheme (UES) could possibly unify many observations related to active galactic nuclei (AGN's), namely quasars, Seyferts, Liners and extended radio sources (ERS's). When the relationship between CEROs and galaxies is so understood, a possible link between galaxies and particles emerges: if galaxies not only emit CEROs but are also able to absorb them by a mechanism seen as the time-reversal of the ejection process, then they should interact with each other via CERO exchange. This process would be similar to photon exchange between electrons, where spiral galaxies and CEROs are considered as cosmic scale electrons and photons respectively. Giant elliptical galaxies would reproduce neutrons and protons exchange. Such a fractal model relating particles to galaxies allows the computation of scaling factors with respect to length, time, velocity, mass and angular momentum, with relatively good agreement between various tests of the model. The CERO speed with respect to the intergalactic medium (IGM) should be a constant and fall in the range 1000-4000 km/s. Finally, the CERO exchange force between two spiral galaxies is evaluated and it is shown to be greater than the conventional gravitational interaction. In analogy with the particle scale. New gravitational constants must be defined for each scale, and with the value found for the particle scale, the particle Planck mass, length and time fall respectively very close to the proton mass, the proton Compton length and the proton Zitterbewegung characteristic time.